Layout pattern proximity correction through fast edge placement error prediction

ABSTRACT

Disclosed are methods of generating a proximity-corrected design layout for photoresist to be used in an etch operation. The methods may include identifying a feature in an initial design layout, and estimating one or more quantities characteristic of an in-feature plasma flux (IFPF) within the feature during the etch operation. The methods may further include estimating a quantity characteristic of an edge placement error (EPE) of the feature by comparing the one or more quantities characteristic of the IFPF to those in a look-up table (LUT, and/or through application of a multivariate model trained on the LUT, e.g., constructed through machine learning methods (MLM)) which associates values of the quantity characteristic of EPE with values of the one or more quantities characteristics of the IFPF. Thereafter, the initial design layout may be modified based on at the determined quantity characteristic of EPE.

BACKGROUND

The performance of plasma-assisted etch processes is frequently criticalto the success of a semiconductor processing workflow. However,optimizing the etch processes can be difficult and time-consuming,oftentimes involving process engineers manually tweaking etch processparameters in an ad hoc fashion in attempt to generate the desiredtarget feature profile. There is currently simply no automated procedureof sufficient accuracy which may be relied upon by process engineers todetermine the values of process parameters which will result in a givendesired etch profile.

Some models attempt to simulate the physical chemical processesoccurring on semiconductor substrate surfaces during etch processes.Examples include the etch profile models of M. Kushner and co-workers aswell as the etch profile models of Cooperberg and co-workers. The formerare described in Y. Zhang, “Low Temperature Plasma Etching Controlthrough Ion Energy Angular Distribution and 3-Dimensional ProfileSimulation,” Chapter 3, dissertation, University of Michigan (2015), andthe latter in Cooperberg, Vahedi, and Gottscho, “Semiempirical profilesimulation of aluminum etching in a Cl₂/BCl₃ plasma,” J. Vac. Sci.Technol. A 20(5), 1536 (2002), each of which is hereby incorporated byreference in its entirety for all purposes. Additional description ofthe etch profile models of M. Kushner and co-workers may be found in J.Vac. Sci. Technol. A 15(4), 1913 (1997), J. Vac. Sci. Technol. B 16(4),2102 (1998), J. Vac. Sci. Technol. A 16(6), 3274 (1998), J. Vac. Sci.Technol. A 19(2), 524 (2001), J. Vac. Sci. Technol. A 22(4), 1242(2004), J. Appl. Phys. 97, 023307 (2005), each of which is also herebyincorporated by reference in its entirety for all purposes. Despite theextensive work done to develop these models, they do not yet possess thedesired degree of accuracy and reliability to find substantial usewithin the semiconductor processing industry.

SUMMARY

Disclosed are methods of generating a proximity-corrected design layoutfor photoresist to be used in an etch operation. The methods may includereceiving an initial design layout and identifying a feature in theinitial design layout, the feature's pattern corresponding to a featurethat would be etched into a material stack on a semiconductorsubstrate's surface via a plasma-based etch process, performed in aprocessing chamber under a set of process conditions, when the stack isoverlaid with a layer of photoresist pattern corresponding to the designlayout. The methods may further include estimating one or morequantities characteristic of an in-feature plasma flux (IFPF) within thefeature at a time t during such a plasma-based etch process, andestimating a quantity characteristic of edge placement error (EPE) ofthe edge of the feature at time t by comparing the one or more estimatedquantities characteristic of the IFPF to those in a look-up table (LUT)which associates values of the quantity characteristic of EPE at time twith values of the one or more quantities characteristics of the IFPF.Thereafter, the initial design layout may be modified based on thequantity characteristic of EPE.

In some embodiments, the LUT is constructed by running a computerizedetch profile model (EPM) under the set of process conditions at least totime t on a calibration pattern of photoresist overlaid on the materialstack. In some embodiments, various of the foregoing operations may berepeated for one or more additional features whose patterns are in theinitial design layout, and the initial design may be modified furtherbased on the estimated quantity characteristic of EPE corresponding tothese one or more additional features.

In some embodiments, the one or more quantities characteristic of theIFPF may include a quantity characteristic of in-feature plasma ion flux(IFPIF), and/or a quantity characteristic of in-feature plasma neutralflux (IFPNF). In some embodiments, the LUT comprises a list of entries,at least some of these entries comprising fields for the quantitycharacteristic of IFPIF, the quantity characteristic of IFPNF, and thecorresponding quantity characteristic of EPE. In some embodiments, atleast some of the entries in the LUT further comprise one or more fieldsfor etch time and/or feature depth. In some embodiments, at least someof the entries in the LUT further comprises a field for in-featurepassivant deposition flux (IFPDF). In some embodiments, at least some ofthe entries in the LUT further comprise a field for edge shape indicatorwhich corresponds to an edge shape present in the calibration pattern.In various embodiments, one or more of the parameters IFPIF, IFPNF,IFPDF, etch time, etch depth, and edge shape serve as independentvariables, and EPE serves as a dependent variable or result. In suchembodiments, many different forms of relationship between independentvariables and the EPE may be employed. These include regression models,neural networks, classification trees (e.g., random forests models), andthe like. The concept of a LUT may be viewed as including any of these.

An aspect of this disclosure pertains to methods of generating a look-uptable associating, for a plurality of features on a semiconductorsubstrate surface, values of one or more quantities characteristic of anedge placement error with values of one or more quantitiescharacteristic of in-feature plasma flux. The features are to be etchedinto a material on the substrate via a plasma-based etch processperformed in a processing chamber under a set of process conditions. Themethod may be characterized by the following features: (a) receiving theset of process conditions and the material composition; (b) receiving apattern of photoresist defining a set of features; (c1) calculating afirst IFPF-characteristic (IFC) value, the first IFC value correspondingto a first quantity characteristic of IFPF during the etch (under theset of process conditions) of a first selected feature from the set offeatures; (c2) calculating a second IFC value, the second IFC valuecorresponding to the first characteristic of IFPF during the etch (underthe set of process conditions) of a second selected feature from the setof features; (d1) including a first entry in the LUT associated with anedge of the first selected feature; and (d2) determining to not includean entry in the LUT associated with an edge of the second selectedfeature and comprising the second IFC value, the determining based (atleast in part) on the similarity of the second IFC value to the firstIFC value. In certain embodiments, the received set of processconditions include global processing chamber plasma fluxes of ion and/orneutral/radical plasma species.

In some embodiments, the methods of this aspect include the followingadditional operations: (c3) calculating a third IFC value, the third IFCvalue corresponding to the first quantity characteristic of IFPF duringthe etch (under the set of process conditions) of a third selectedfeature from the set of features; and (d3) determining to not include anentry in the LUT associated with an edge of the third selected featureand comprising the third IFC value, the determining based (at least inpart) on the similarity of the third IFC value to the first IFC value.

In some embodiments, the methods of this aspect include the followingadditional operations: (c1′) calculating a third IFC value, the thirdIFC value corresponding to a second quantity characteristic of IFPFduring the etch (under the set of process conditions) of the firstselected feature; and (c2′) calculating a fourth IFC value, the fourthIFC value corresponding to the second quantity characteristic of IFPFduring the etch (under the set of process conditions) of the secondselected feature. In (d1), the first entry in the LUT further comprisesthe third IFC value, and in (d2), the determining is further based onthe similarity of the fourth IFC value to the third IFC value.

In (d2), the determining may be based (at least in part) on a distancemetric calculated between the first selected feature and the secondselected feature, the distance metric. Such distance metric may becalculated by a procedure including: (i) calculating a first differenceindicator (DI) value indicative of the difference between the first IFCvalue and the second IFC value; (ii) calculating a second DI valueindicative of the difference between the third IFC value and the fourthIFC value; and (iii) calculating a combined DI value indicative of thesum of the magnitudes of the first DI value and the second DI value. Insome cases, in (d2) the determining includes comparing the distancemetric to a reference value.

In certain embodiments, in (d2), the determining is further based on thesimilarity of the first EPC value to a second EPC value, whichcorresponds to a quantity characteristic of an EPE of the edge of thesecond selected feature. The second EPC value may be generated byrunning a computerized etch profile model (EPM) to simulate etchingunder the set of process conditions of the material as overlaid with atleast the portion of the pattern of photoresist corresponding to thesecond selected feature.

In some embodiments, the first quantity characteristic of IFPF is moreparticularly characteristic of in-feature plasma ion flux (IFPIF).Further, the first IFC value may be estimated based on a visibilitykernel (VC) corresponding to the feature. In such case, the first IFCmay be calculated by a procedure comprising estimating the integral ofthe VC with the ion energy angular distribution function (IEADF)corresponding to one or more plasma ion fluxes (PIF) above the feature.

In certain embodiments, the first quantity characteristic of IFPF ismore particularly characteristic of in-feature plasma neutral flux(IFPNF). Further, the quantity characteristic of IFPNF may be a loadedplasma flux above the feature which accounts for the presence of thesubstrate in the processing chamber.

In certain embodiment, in (d2), the determining is further based on: (i)a sensitivity metric characteristic of the magnitude of variations inthe first EPC value which result from changes in the first IFC value;and/or (ii) a sensitivity metric characteristic of the magnitude ofvariations in a second EPC value which result from changes in the secondIFC value, which corresponds to a quantity characteristic of an EPE ofthe edge of the second selected feature. The value is generated byrunning a computerized etch profile model (EPM) to simulate etchingunder the set of process conditions of the material as overlaid with atleast the portion of the pattern of photoresist corresponding to thesecond selected feature. Further, the sensitivity metric characteristicof either or both of the first or second EPC values may be calculated byestimating the partial derivative of the quantity characteristic of EPEwith respect to the first quantity characteristic of IFPF(d[EPE]/d[IFPF]) evaluated at either the first or second values of theEPC and IFC. Additionally, the sensitivity metric may be calculated by aprocess including:

-   -   calculating a first difference indicator (DI) value indicative        of the difference between the first and second EPC values;    -   calculating a second DI value indicative of the difference        between the first and second IFC values; and    -   calculating a value indicative of d[EPE]/d[IFPF] by calculating        a value indicative of the ratio of the second to the first DI        values.

In certain embodiments, in (d2) the determining includes comparing thesensitivity metric to a reference value.

In such embodiments, the first quantity characteristic of IFPF may bemore particularly characteristic of in-feature plasma ion flux (IFPIF).In such embodiments, the first quantity characteristic of IFPF may bemore particularly characteristic of in-feature plasma neutral flux(IFPNF).

Another aspect of the disclosure pertains to look-up tables (LUTs)including a plurality of entries corresponding to a plurality of edgesof a plurality of features to be etched into a material on asemiconductor substrate surface via a plasma-based etch processperformed in a processing chamber under a set of process conditions. Theentries of the LUT include a plurality of fields, which include (a) anEPE field holding a value of a quantity characteristic of an edgeplacement error (EPE); and (b) one or more IFPF fields holding values ofone or more quantities characteristic of an in-feature plasma flux(IFPF). Examples of the IFPF fields include an IFPIF field for holding avalue of a quantity characteristic of in-feature plasma ion flux(IFPIF); an IFPNF field for holding a value of a quantity characteristicof in-feature plasma neutral flux (IFPNF); and an IFPDF field forholding a value of a quantity characteristic of in-feature passivantdeposition flux (IFPDF). In certain embodiments, the average relativedifference between pairs of nearest values held in fields of the tablecorresponding to each quantity characteristic of IFPF is greater than adefined amount (e.g., about 5%.)

Another aspect of the disclosure pertains to methods of identifying asubset of entries from a set of potential entries for use in a look-uptable (LUT) or other framework for characterizing an etch process, theentries corresponding to a plurality of edges of a plurality of featuresto be etched into a material on a semiconductor substrate surface via aplasma-based etch process performed in a processing chamber under a setof process conditions. Each entry includes:

-   -   a value of a quantity characteristic of an edge placement error        (EPE) of an edge of a feature; and    -   a value of a quantity characteristic of an in-feature plasma        flux (IFPF) during said etching of the feature.

The method may be characterized by the following operations:

-   -   for each potential entry, calculating a sensitivity metric for        the entry, the sensitivity metric indicative of the magnitude of        the partial derivative of the quantity characteristic of EPE        with respect to the quantity characteristic of IFPF        (d[EPE]/d[IFPF]) evaluated at the value of the quantity        characteristic of IFPF; and    -   selecting a subset of entries from the set of potential entries        such that the average of the sensitivity metric over the subset        is higher than the average of the sensitivity metric over the        full set.

In such methods, the value of the quantity characteristic of the EPE ofeach entry may be generated by running a computerized etch profile model(EPM) to simulate etching under the set of process conditions of thematerial as overlaid with at least the portion of the pattern ofphotoresist corresponding to a particular feature. In some embodiments,the subset of entries is selected such that of the 25% of the entries inthe full set having the highest sensitivity metrics, at least 5% areincluded in the subset. In some embodiments, the subset of entries isselected such that when the subset is sorted based on the quantitycharacteristic of IFPF, the density of entries in the subset (relativeto the quantity characteristic of IFPF) changes in proportion to theaverage sensitivity metric (calculated over the group of entries withinthe subset used to estimate the density) over at least about 75% of theentries selected for the subset. In certain embodiments, the quantitycharacteristic of IFPF is an in-feature plasma ion flux (IFPIF); anin-feature plasma neutral flux (IFPNF); or an in-feature passivantdeposition flux (IFPDF).

Another aspect of the disclosure pertains to methods of detecting highsensitivity regions in a plurality of features to be etched into amaterial on a semiconductor substrate surface via a plasma-based etchprocess performed in a processing chamber under a set of processconditions. A high sensitivity region corresponds to an edge of afeature which is particularly sensitive to etch process conditions. Themethods may be characterized by the following operations:

-   -   choosing a plurality of potential high sensitivity regions in        the plurality of features, each potential high sensitivity        region corresponding to a particular edge of a feature;    -   for each potential high sensitivity region, calculating a        sensitivity metric corresponding to the particular edge        associated with the potential high sensitivity region, the        sensitivity metric indicative of the magnitude of an estimated        partial derivative of a quantity characteristic of an edge        placement error (EPE) corresponding to the edge with respect to        a quantity characteristic of an in-feature plasma flux (IFPF)        corresponding to the feature, said partial derivative estimated        with respect to a value of said quantity characteristic of IFPF        corresponding to the feature and chosen process conditions; and    -   identifying high sensitivity regions in the plurality of        potential high sensitivity regions based on the sensitivity        metric.

Also disclosed herein are methods of generating a mask design. Thesemethods may include generating a proximity-corrected design layout forphotoresist using the techniques just described, and thereaftergenerating a mask design based on the generated proximity-correctedphotoresist design layout. Also disclosed herein are methods of etchinga semiconductor substrate. These methods may include generating a maskdesign as just described and forming a mask based on the mask design.Thereafter, a photolithography operation may be performed using the maskto transfer a layer of photoresist to the substrate substantiallyconforming to the proximity-corrected photoresist design layout, afterwhich the substrate may be exposed to a plasma which finally etches thesubstrate.

Also disclosed are computer systems for generating a proximity-correcteddesign layout for photoresist to be used in an etch operation. Thesystems may include a processor and a memory. The memory may store alook-up table (LUT) and computer-readable instructions for execution onthe processor. The instructions stored in the memory may includeinstructions for receiving an initial design layout, and instructionsfor identifying a feature in the initial design layout, the feature'spattern corresponding to a feature that would be etched into a materialstack on a semiconductor substrate's surface via a plasma-based etchprocess, performed in a processing chamber under a set of processconditions, when the stack is overlaid with a layer of photoresistpattern corresponding to the design layout. The instructions stored inthe memory may further include instructions for estimating one or morequantities characteristic of an in-feature plasma flux (IFPF) within thefeature at a time t during such a plasma-based etch process,instructions for estimating a quantity characteristic of edge placementerror (EPE) of the edge of the feature at time t by comparing the one ormore quantities characteristic of the IFPF estimated in (c) to those inthe LUT which associates values of the quantity characteristic of EPE attime t with values of the one or more quantities characteristics of theIFPF, and instructions for modifying the initial design layout based onat the quantity characteristic of EPE.

In some embodiments, the initial design layout may be read from acomputer-readable medium, and in certain such embodiments, thecomputer-readable instructions stored in the memory for execution on theprocessor further include instructions for writing theproximity-corrected design layout to a computer-readable medium.

Also disclosed herein are one or more computer-readable media having alook-up table (LUT) and computer-readable and executable instructions asjust described stored thereon.

Also disclosed are systems for generating photolithography masks. Suchsystems may include a computer system for generating aproximity-corrected design layout for photoresist as just described, anda photolithography module. The photolithography module may be configuredto receive a proximity-corrected design layout for photoresist from thecomputer system, and form a mask from the proximity-corrected designlayout. Also disclosed are systems for etching semiconductor substratesusing such masks to perform photolithography operations by transferringthe proximity-corrected design layout to a layer of photoresist on asemiconductor substrate. Such systems may further include aplasma-etcher configured to generate a plasma which may be used tocontact the semiconductor substrate and etch those portions of thesubstrate surface not covered with photoresist patterned using the mask.

These and other features of the disclosure will be described below withreference to the associated drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 represents an example of an etch profile as generatedcomputationally from a surface kinetic model of an etch process.

FIG. 2 represents an example of an etch profile, similar to that shownin FIG. 1, but in this figure, computed from experimental measurementsmade with one or more optical metrology tools.

FIG. 3 is a process flow chart representing procedures for optimizingetch profile models with respect to a etch profile coordinate space.

FIG. 4A is a process flow chart representing procedures for optimizingetch profile models, and particularly certain model parameters used insuch models.

FIG. 4B is a process flow chart representing procedures for optimizingetch profile models, and particularly certain model parameters used insuch models.

FIG. 5 depicts an example set of canonical etch profiles that may beidentified using models optimized in accordance with this disclosure.

FIG. 6 is a process flow chart representing procedures for optimizingetch profile models with respect to a reflectance spectral space.

FIG. 7A is an illustration of the reflectance spectral history of anetch profile as it evolves during an etch process.

FIG. 7B schematically presents a set of spectral reflectance datacollected over many wafers in the form of a 3-D data block (the 3indices of the data block correspond to wafer number (i), spectralwavelength (j), and etch process time (k)); as well as the 3-D datablock's unfolding into a 2-D data block which may serve as theindependent data for the PLS spectral history analysis, the dependentdata being the etch profile coordinates also indicated in the figure.

FIG. 8 is a process flow chart illustrating an iterative procedure foroptimizing a PLS model relating etch spectral reflectance history toetch profiles over the course of an etch process while concurrentlyoptimizing a EPM, which is used in the generation of computedreflectance spectra to be employed in the optimization of the PLS model.

FIGS. 9A-9C illustrate an embodiment of an adjustable-gapcapacitively-coupled (CCP) plasma reactor.

FIG. 10 illustrates an embodiment of an inductively-coupled plasma (ICP)reactor.

FIG. 11A shows a cross-sectional view of a 2-layer stack of material ona semiconductor substrate before and after a feature is etched into it,as defined by a layer of photoresist.

FIG. 11B shows a top-view of a trench feature having a 90 degree turn.

FIG. 12 shows the various phases of the standard empirical VEB approachto pattern proximity correction (PPC) and illustrates a timeline (inunits of weeks) for completion of the various phases, as well as forcompletion of the entire VEB-based mask build process. FIG. 12 alsoshows a similar timeline when instead using a physics-based etch profilemodel approach as disclosed herein.

FIG. 13A provides an illustration of a simple calibration pattern withcertain structures/features selected from it.

FIG. 13B provides an illustration of a reduced-order model (ROM) look-uptable (LUT) as described herein.

FIG. 13C provides an illustration of another reduced-order model (ROM)look-up table (LUT) as described herein.

FIGS. 14A and 14B both display a feature/structure of a semiconductorsubstrate labeled with the quantities held in the fields of the ROMlook-up table (LUT).

FIG. 15 shows a sequence of operations for generating a patternproximity-corrected design layout for photoresist.

FIG. 16 shows a sequence of operations for generating a patternproximity-corrected design layout for photoresist involving calculatingan edge placement error (EPE) of multiple features in the initial designlayout.

FIG. 17 shows a cross-sectional view of a feature with lines-of-sightdrawn to illustrate the visibility of a point within the feature, forexample, to directional ion flux.

FIG. 18 shows a sequence of operations for generating a patternproximity-corrected design layout for photoresist involving refiningestimated feature visibility as part of calculating edge placement error(EPE).

FIGS. 19A and 19B show a cross-sectional view of a feature andillustrate a single-time-step approach to edge-placement error (EPE)estimation versus a multi-time step approach.

FIG. 20 shows a multi-time step sequence of operations for generating apattern proximity-corrected design layout for photoresist.

FIG. 21 is a graphical representation of the results of a down selectionprocess that reduces the number of entries in a LUT (pruning).

FIG. 22 is a flow chart of a method that uses down selection to reducethe size of a LUT.

FIG. 23A shows a process flow diagram depicting an embodiment forgenerating EPEs from features found on test mask, and then downselecting the generated EPEs (and associated LUT entries).

FIGS. 23B-23E present details of certain operations in the flow diagramof FIG. 23A.

FIG. 24 illustrates in a general format how information for downselecting LUT entries may be collected.

DETAILED DESCRIPTION Terminology

The following terms are used in the instant specification.

Independent variable—as commonly understood, an independent variable isany variable that causes a response. An independent variable may also beknown as a “predictor variable,” “regressor,” “controlled variable,”“manipulated variable,” “explanatory variable,” or “input variable.” Anetch profile model may include various types of independent variablessuch as reactor process conditions (e.g., temperature, pressure, gascomposition, flow rates, plasma power, and the like), local plasmaconditions, and local reaction conditions. A LUT or other relationshipdescribed herein may employ IFPF parameters, etch times, feature edgeshapes, and the like as independent variables.

Result variable—as commonly understood, a result variable is a variablethat results from the independent variables. Often a result model isoutput by a model. In some contexts, a result variable is synonymouswith the term dependent variable. In this disclosure an etch profile isa type of result variable. An edge placement error is another type ofresult variable.

Input variable—an input variable is similar to an independent variable,but may be more specific in that some independent variables may be fixedfor many runs and therefore not technically “input” variables for suchruns. In input variable is provided as an input for a run underconsideration.

Mechanistic parameter—a mechanistic parameter is a type of independentvariable that represents a physical and/or chemical condition at one ormore particular locations in a reactor or substrate undergoing etching.

Plasma parameter—a plasma parameter is a type of mechanistic parameterdescribing local plasma conditions (e.g., plasma density and plasmatemperature at particular locations on the substrate).

Reaction parameter—a reaction parameter is a type of mechanisticparameter describing a local chemical or physico-chemical condition.

Process parameter—a process parameter is a reactor parameter over whichthe process engineer has control (e.g., chamber pressure, RF power, biasvoltage, gas flow rates, and pedestal temperature). Process parametersalong with substrate characteristics may control values of themechanistic parameters in an etch reactor.

Model parameter—a model parameter is a type of independent variable thatis optimized. It is typically a mechanistic parameter such as a chemicalreaction parameter. Initial values of model parameters are typicallyunoptimized; they may be estimates chosen based on expert knowledge orselected from literature data.

Introduction—Etch Profile Models

Disclosed herein are procedures for using etch profile models (EPMs)referred to above (and other similar models) to generate accuraterepresentations of semiconductor feature etch profiles, which are goodenough approximations to be relied upon in the semiconductor processingindustry.

Generally, EPMs and similar models attempt to simulate the etch profileevolution of a substrate feature over time—i.e., the time-dependentchanges in the shape of a feature at various spatial locations on thefeature's surface—by calculating reaction rates associated with the etchprocess at each of these spatial locations which result from an incidentflux of etchant and deposition species characteristic of the plasmaconditions set up in the reaction chamber, and do so over the course ofthe simulated etch process. The output is a simulated etch profilerepresented by a discrete set of data points—i.e., profilecoordinates—which spatially maps out the shape of the profile. Anexample of such a simulated etch profile is shown in FIG. 1; thesimulated profile may correspond to an actual measured etch profile asshown in FIG. 2. The simulated etch profile's evolution over timedepends on the theoretically-modelled, spatially-resolved local etchreaction rates which, of course, depend on the underlying chemistry andphysics of the etch process. As such, the etch profile simulationdepends on various physical and chemical parameters associated with thechemical reaction mechanisms underlying the etch processes, and also anyphysical and chemical parameters which may characterize the chamberenvironment—temperature, pressure, plasma power, reactant flow rate,etc.—which are, generally speaking, under the control of the processengineer.

With respect to the former, the etch profile model thus requires a setof “fundamental” chemical and physical input parameters—examples such asreaction probabilities, sticking coefficients, ion and neutral fluxes,etc.—which are generally not independently controllable and/or evendirectly knowable by the process engineer, but that nevertheless must bespecified as inputs to the simulation. These sets of “fundamental” or“mechanistic” input parameters are thus assumed to have certain values,generally taken from the literature, and their use implicitly invokescertain simplifications of (and approximations to) the underlyingphysical and chemical mechanisms behind the etch process being modeled.

This disclosure presents procedures that combine experimental techniquesand data mining/analysis methodologies to improve the practicalindustrial applicability of these EPMs of substrate etch processes. Notethat the phrase “substrate etch process” includes processes which etch amask layer or, more generally, processes which etch any layer ofmaterial having been deposited on and/or residing on a substratesurface. The techniques focus on the “fundamental” chemical and physicalinput parameters which are employed by these models and improve themodels by using procedures to determine what may be viewed as moreeffective sets of values for these parameters—effective in the sensethat they improve the accuracy of the etch model even if the optimumvalues determined for these “fundamental” parameters differ than whatthe literature (or other experiments) might determine as the “true”physical/chemical values for these parameters.

FIGS. 3 and 4, which are discussed more fully below, present flow chartsillustrating example processes for generating improved etch profilemodels. In FIG. 3, for example, the depicted process flow has two inputbranches, one from experimental measurements and the other from acurrent version of the model, which version is not yet optimized. Boththe experimental branch and the predictive model branch produce etchprofile results. These results are compared and the comparison is usedto improve the model so that the deviation between the resultsdecreases.

Characterizing etch profile data in detail, in 2 or 3 dimensions asoutput by an EPM, presents particular challenges for optimizing themodel. In various embodiments disclosed herein, the profile data isrepresented as a series of elevation slices, each having a thickness. Inother embodiments, the profile is represented as a series of vectorsfrom a common origin or as a series of geometric forms such astrapezoids. When using many of these elevation slices or othercomponents of the profile, the optimization problem of minimizing theerror between experimental and EPM profile, can be computationallydemanding. To reduce the required computation, a dimension reductiontechnique such as principal component analysis (PCA) is used to identifycorrelated contributions from the various profile components to theoverall physical profile used in the optimization. Presenting the etchprofiles in a few principal components or other vectors in a reduceddimensional space can greatly simplify the process of improving thepredictive capabilities of the etch profile models. Additionally, suchprinciple components are orthogonal to one another which assures thatindependent profile contributions can be optimized in isolation.

Etch Profiles

Before delving into the details of the etch profile models and theprocedures for their improvement, it is useful to describe the conceptof a feature's etch profile. Generally, an etch profile (EP) refers toany set of values for a set of one or more geometric coordinates whichmay be used to characterize the shape of an etched feature on asemiconductor substrate. In a simple case, an etch profile can beapproximated as the width of a feature determined halfway to the base ofthe feature (the midpoint between the feature's base (or bottom) andit's top opening on the surface of the substrate) as viewed through a2-dimensional vertical cross-sectional slice through the feature. In amore complicated example, an etch profile may be series of featurewidths determined at various elevations above the base of the feature asviewed through the same 2-dimensional vertical cross-sectional slice.FIG. 2 provides an illustration of this. Note that, depending on theembodiment, the width may be the distance between one sidewall of therecess feature and the other—i.e. the width of the region which has beenetched away—or the width may refer to the width of a column which hasbeen etched on either side. The latter is schematically illustrated inFIG. 2. Note that in some cases, such a width is referred to as a“critical dimension” (labeled “CD” in FIG. 2) and that the elevationfrom the base of the feature may be referred to as the height or thez-coordinate (labeled as percentages in FIG. 2) of the so-referred-tocritical dimension. As mentioned, the etch profile may be represented inother geometric references such as by a group of vectors from a commonorigin or a stack of shapes such as trapezoids or triangles or a groupof characteristic shape parameters that define a typical etch profilesuch as bow, straight or tapered sidewall, rounded bottom, facet etc.

In this way, a series of geometric coordinates (e.g., feature widths atdifferent elevations) maps out a discretized portrayal of a feature'sprofile. Note, that there are many ways to express a series ofcoordinates which represent feature width at different elevations. Forinstance, each coordinate might have a value which represents afractional deviation from some baseline feature width (such as anaverage feature width, or a vertically averaged feature width), or eachcoordinate might represent the change from the vertically adjacentcoordinate, etc. In any event, what is being referred to as “width” and,generally, the scheme being used for the set of profile coordinates usedto represent an etch profile will be clear from the context and usage.The idea is that a set of coordinates are used to represent the shape ofthe feature's etched profile. It is also noted that a series ofgeometric coordinates could also be used to describe the full3-dimensional shape of a feature's etched profile or other geometriccharacteristic, such as the shape of an etched cylinder or trench on asubstrate surface. Thus, in some embodiments, a etch profile model mayprovide a full 3-D etch shape of the feature being modeled.

Etch Profile Models

The etch profile models (EPMs) compute a theoretically determined etchprofile from a set of input etch reaction parameters (independentvariables) characterizing the underlying physical and chemical etchprocesses and reaction mechanisms. These processes are modelled as afunction of time and location in a grid representing features beingetched and their surroundings. Examples of input parameters includeplasma parameters such as fluxes of gas phase species—ions, neutrals,radicals, photons, etc.—and surface chemical reaction parameters such asthe reaction probability, threshold energy, sputter yield correspondingto a particular chemical reaction. These parameters (and particularly,in some embodiments, the plasma parameters) may be obtained from varioussources, including other models which calculate them from generalreactor configurations and process conditions such as pressure,substrate temperature, plasma source parameters (e.g., power,frequencies, duty cycles provided to the plasma source), reactants, andtheir flow rates. In some embodiments, such models may be part of theEPM.

As explained, EPMs take reaction parameters as independent variables andfunctionally generate etch profiles as response variables. In otherwords, a set of independent variables are the physical/chemical processparameters used as inputs to the model, and response variables are theetch profile features calculated by the model. The EPMs employ one ormore relationships between the reaction parameters and the etch profile.The relationships may include, e.g., coefficients, weightings, and/orother model parameters (as well as linear functions of, second andhigher order polynomial functions of, etc. the reaction parametersand/or other model parameters) that are applied to the independentvariables in a defined manner to generate the response variables, whichare related to the etch profiles. Such weightings, coefficients, etc.may represent one or more of the reaction parameters described above.These model parameters are tuned or adjusted during the optimizationtechniques described herein. In some embodiments, some of the reactionparameters are model parameters to be optimized, while others are usedas independent input variables. For example, chemical reactionparameters may be optimizable model parameters, while plasma parametersmay be independent variables.

In general, a “response variable” represents an output and/or effect,and/or is tested to see if it is the effect. An “independent variable”represents an inputs and/or causes, and/or is tested to see if it is thecause. Thus, a response variable may be studied to see if and how muchit varies as the independent variables vary.

As explained, some EPMs employ input variables (a type of independentvariables) that may be characterized as fundamental reaction mechanisticparameters and may be viewed as fundamental to the underlying chemistryand physics and therefore the experimental process engineer generallydoes not have control over these quantities. In the etch profile model,these variables are applied at each location of a grid and at multipletimes, separated by defined time steps. In some implementations, thegrid resolution may vary between about a few Angstroms and about amicrometer. In some implementations, the time steps may vary betweenabout 1e-15 and 1e-10 seconds. In certain embodiments, the optimizationemploys two types of mechanistic independent variables: (1) local plasmaparameters, and, and (2) local chemical reaction parameters. Theseparameters are “local” in the sense that they may vary a function ofposition, in some cases down to the resolution of the grid. Examples ofthe plasma parameters include local plasma properties such as fluxes andenergies of particles such ions, radicals, photons, electrons, excitedspecies, depositor species and their energy and angular distributionsetc. Examples of chemical and physico-chemical reaction parametersinclude rate constants (e.g., probabilities that a particular chemicalreaction will occur at a particular time), sticking coefficients, energythreshold for etch, reference energy, exponent of energy to definesputter yields, angular yield functions and its parameters, etc.Further, the parameterized chemical reactions include reactions in whichthe reactants include the material being etched and an etchant. Itshould be understood that the chemical reaction parameters may includevarious types of reactions in addition to the reactions that directlyetch the substrate. Examples of such reactions include side reactions,including parasitic reactions, deposition reactions, reactions ofby-products, etc. Any of these might affect the overall etch rate. Itshould also be understood that the model may require other inputparameters, in addition to the above-mentioned plasma and chemicalreaction input parameters. Examples of such other parameters include thetemperature at the reaction sites, the partial pressure or reactants,etc. In some cases, these and/or other non-mechanistic parameters may beinput in a module that outputs some of the mechanistic parameters.

In some embodiments, initial (unoptimized) values for the EPM modelvariables, as well as independent variables that are fixed duringoptimization (e.g., the plasma parameters in some embodiments) may beobtained from various sources such as the literature, calculations byother computational modules or models, etc. In some embodiments, theindependent input variables—such as the plasma parameters—may bedetermined by using a model such as, for the case of the plasmaparameters, from an etch chamber plasma model. Such models may calculatethe applicable input EPM parameters from various process parameters overwhich the process engineer does have control (e.g., by turning aknob)—e.g., chamber environment parameters such as pressure, flow rate,plasma power, wafer temperature, ICP coil currents, bias voltages/power,pulsing frequency, pulse duty cycle, and the like.

When running an EPM, some of the independent variables are set to knownor expected parameter values used to perform the experiments. Forexample, the plasma parameters may be fixed to known or expected valuesat locations in modeled domain. Other independent variables—describedherein as parameters of the model or the model parameters—are thosewhich are selected to be tuned by the optimization procedure describedbelow. For example, the chemical reaction parameters may be the tunedmodel parameters. Thus, in a series of runs corresponding to a givenmeasured experimental etch profile, the model parameters are varied inorder to elucidate how to choose values of these parameters to bestoptimize the model.

EPMs may take any of many different forms. Ultimately, they provide arelationship between the independent and response variables. Therelationship may be linear or nonlinear. Generally, an EPM is what isreferred to in the art as a Monte Carlo surface kinetic model. Thesemodels, in their various forms, operate to simulate a wafer feature'stopographical evolution over time in the context of semiconductor waferfabrication. The models may utilize a cell-based representation of thetopological evolution, but may also used a level-set type model, or acombination of the foregoing. Moreover, lumped kinetic models may alsobe employed such as lumped Langmuir-Hinshelwood kinetic models or othertypes of semi-analytical hybrid models. The models launchpseudo-particles with energy and angular distributions produced by aplasma model or experimental diagnostics for arbitrary radial locationson the wafer. The pseudo-particles are statistically weighted torepresent the fluxes of radicals and ions to the surface. The modelsaddress various surface reaction mechanisms resulting in etching,sputtering, mixing, and deposition on the surface to predict profileevolution. During a Monte Carlo integration, the trajectories of variousion and neutral pseudo-particles are tracked within a wafer featureuntil they either react or leave the computational domain. The EPM hasadvanced capabilities for predicting etching, stripping, atomic layeretching, ionized metal physical vapor deposition, and plasma enhancedchemical vapor deposition on various materials. In some embodiments, anEPM utilizes a rectilinear mesh in two or three dimensions, the meshhaving a fine enough resolution to adequately address/model thedimensions of the wafer feature (although, in principle, the mesh(whether 2D or 3D) could utilize non-rectilinear coordinates as well).The mesh may be viewed as an array of grid-points in two or threedimensions. It may also be viewed as an array of cells which representthe local area in 2D, or volume in 3D, associated with (centered at)each grid-point. Each cell within the mesh may represent a differentsolid material or a mixture of materials. Whether a 2D or 3D mesh ischosen as a basis for the modeling may depend on the class/type of waferfeature being modelled. For instance, a 2D mesh may be used to model along trench feature (e.g., in a polysilicon substrate), the 2D meshdelineating the trench's cross-sectional shape under the assumption thatthe geometry of the ends of the trench are not too relevant to thereactive processes taking place down the majority of the trench's lengthaway from its ends (i.e., for purposes of this cross-sectional 2D model,the trench is assumed infinite, again a reasonable assumption for atrench feature away from its ends). On the other hand, it may beappropriate to model a circular via feature (a through-silicon via(TSV)) using a 3D mesh (since the x,y horizontal dimensions of thefeature are on par with each other).

Mesh spacing may range from sub-nanometer (e.g., from 1 Angstrom) up toseveral micrometers (e.g., 10 micrometers). Generally, each mesh cell isassigned a material identity, for example, photoresists, polysilicon,plasma (e.g., in the spatial region not occupied by the feature), whichmay change during the profile evolution. Solid phase species arerepresented by the identity of the computational cell; gas phase speciesare represented by computational pseudo-particles. In this manner, themesh provides a reasonably detailed representation (e.g., forcomputational purposes) of the wafer feature and surrounding gasenvironment (e.g., plasma) as the geometry/topology of the wafer featureevolves over time in a reactive etch process.

Etch Experiments and Profile Measurements

To train and optimize the EPMs presented in the previous section,various experiments may be performed in order to determine—as accuratelyas the experiments allow—the actual etch profiles which result fromactual etch processes performed under the various process conditions asspecified by various sets of etch process parameters. Thus, forinstance, one specifies a first set of values for a set of etch processparameters—such as etchant flow rate, plasma power, temperature,pressure, etc.—sets up the etch chamber apparatus accordingly, flowsetchant into the chamber, strikes the plasma, etc., and proceeds withthe etching of the first semiconductor substrate to generate a firstetch profile. One then specifies a second set of values for the same setof etch process parameters, etches a second substrate to generate asecond etch profile, and so forth.

Various combinations of process parameters may be used to present abroad or focused process space, as appropriate, to train the EPM. Thesame combinations of process parameters are then used to calculate(independent) input parameters, such as the mechanistic parameters, tothe EPM to provide etch profile outputs (response variables) that can becompared against the experimental results. Because experimentation canbe costly and time consuming, techniques can be employed to designexperiments in a way that reduces the number of experiments that need beconducted to provide a robust training set for optimizing the EPM.Techniques such as design of experiments (DOE) may be employed for thispurpose. Generally, such techniques determine which sets of processparameters to use in various experiments. They choose the combinationsof process parameters by considering statistical interactions betweenprocess parameters, randomization, and the like. As an example, DOE mayidentify a small number of experiments covering a limited range ofparameters around the center point of a process that has been finalized.

Typically, a researcher will conduct all experiments early in the modeloptimization process and use only those experiments in the optimizationroutine iterations until convergence. Alternatively, an experimentdesigner may conduct some experiments for early iterations of theoptimization and additional experiments later as the optimizationproceeds. The optimization process may inform the experiment designer ofparticular parameters to be evaluated and hence particular experimentsto be run for later iterations.

One or more in-situ or offline metrology tools may be used to measurethe experimental etch profiles which result from these experimental etchprocess operations. Measurements made be made at the end of the etchprocesses, during the etch processes, or at one or more times during theetch processes. When measurements are made at the end of an etchprocess, the measurement methodology may be destructive, when made atintervals during the etch process, the measurement methodology wouldgenerally be non-destructive (so not to disrupt the etch). Examples ofappropriate metrology techniques include, but are not limited to, insitu and ex situ optical critical dimension (OCD) scatterometry andcross-sectional SEM. Note that a metrology tool may directly measure afeature's profile, such as is the case of SEM (wherein the experimentbasically images a feature's etch profile), or it may indirectlydetermine a feature's etch profile, such as in the case of OCDmeasurements (where some post-processing is done to back-out thefeature's etch profile from the actual measured data). Also note, thatin some embodiments, EPM optimization may be done in the spectral spaceand so one would not need to back out the etch profile from the OCDmeasurements; instead one would use the etch profile calculated via theEPM to simulate OCD scattering.

In any event, the result of the etch experiments and metrologyprocedures is a set of measured etch profiles, each generally includinga series of values for a series of coordinates or a set of grid valueswhich represent the shape of the feature's profile as described above.An example is shown in FIG. 2. The etch profiles may then be used asinputs to train, optimize, and improve the computerized etch profilemodels as described below.

Model Parameter Tuning/Optimization

Each measured experimental etch profile provides a benchmark for tuningthe computerized etch profile model. Accordingly, a series ofcalculations are performed with the etch profile model by applying theexperimental etch profiles to see how the model deviates from reality inits prediction of etch profiles. With this information, the model may beimproved.

FIG. 3 presents a flowchart illustrating a set of operations 300 fortuning and/or optimizing an etch profile model, such as those describedabove. In some embodiments, such a tuned and/or optimized modelreduces—and in some cases substantially minimizes—a metric which isrelated to (indicative of, quantifies, etc.) the combined differencesbetween the etch profiles which are measured as a result of performingthe etch experiments, and the corresponding computed etch profiles asgenerated from the model. In other words, an improved model may reducethe combined error over the different experimental process conditions(as designated by the different sets of specified values of the selectedprocess parameters—which are used to compute independent inputparameters to the EPM).

As shown in FIG. 3, the optimization procedure 300 begins at operation310 with the selection of a set of model parameters to be optimized.Again, these model parameters may be chosen to be parameters whichcharacterize the underlying chemical and physical processes over whichthe process engineer has no control. Some or all of these will beadjusted based on the experimental data to improve the model. In someembodiments, these model parameters may be reaction parameters andinclude reaction probabilities and/or (thermal) rate constants, reactantsticking coefficients, etch threshold energies for physical or chemicalsputtering, exponent dependence on energy, etch angular yielddependencies and parameters associated with the angular yield curve,etc. Note that, in general, the optimization is done with respect to aparticular given/specified mixture of chemical species flowed into theetch chamber (though it should be understood that the chemicalcomposition of the etch chamber will change as the etch processproceeds). In some embodiments, the reaction parameters are fed into theEPM in a separate input file from the other input parameters (such asthe plasma parameters).

In some embodiments, the model parameters may include the specificationof which particular chemical reactions are to be modelled by the etchprocess. One of ordinary skill in the art will appreciate that, for agiven etch process, there may be many ongoing reactions occurring in theetch chamber at any time. These include the main etch reaction itself,but it may also include side reactions of the main etch process, andreactions involving by-products of the main etch reaction, reactionsbetween by-products, reactions involving by-products of by-products,etc. Thus, in some embodiments, selection of the model parametersinvolves choosing which reactions to include in the model. Presumably,the more reactions that are included, the more accurate the model, andthe more accurate the corresponding computed etch profile. However,increasing the complexity of the model by including more reactions,increases the computational cost of the simulation. It also results inthere being more reaction parameters to optimize. This may be good ifthe particular reaction which is added is important to the overall etchkinetics. However, if the additional reaction is not critical, theaddition of another set of reaction parameters may make the optimizationprocedure more difficult to converge. Once again, the choices of whichreactions to include and the rate constants or reaction probabilitiesassociated with these reactions may be fed into the EPM in their owninput file (e.g., separate from the plasma parameters). In certainembodiments, for a given set of reactant species, the probabilities ofthe various alternative/competing reaction pathways for each speciesshould sum to unity. And, once again, it should be appreciated that thespecification of reactions to include, reaction probabilities, etc.(e.g., in the input file) would generally be done for a given/specifiedmixture of chemical species which are being flowed into the etch chamberto perform the etch process/reaction (and the optimization wouldgenerally be with respect to this given mixture, though in someembodiments, one can see that what is learned with respect to onechemical mixture, may have applicability to similar/related chemicalmixtures).

In any event, to begin the optimization process shown in the flowchartof FIG. 3, initial values generally must be chosen for the various modelparameters being optimized (such as the reaction probabilities, stickingcoefficients, etc.). This is done in operation 310. The initial valuesmay be those found in the literature, those calculated based on othersimulations, determined from experiment, or known from previousoptimization procedures, etc.

The model parameters chosen and initialized in operation 310 areoptimized over a set of independent input parameters which are givenmultiple sets of values in operation 320. Such independent inputparameters may include parameters which characterize the plasma in thereaction chamber. In some embodiments, these plasma parameters are fedinto the EPM via an input file which is separate from the input fileused for the reaction parameters (just described). The multiple sets ofvalues for the independent input parameters (e.g., plasma parameters)thus specify different points in the space of the selected independentinput parameters. For example, if the input parameters chosen to beoptimized over are temperature, etchant flux, and plasma density, and 5sets of values are chosen for these selected input parameters, then onehas identified 5 unique points in the selected 3-dimensional inputparameter space of temperature, etchant flux, and plasma density—each ofthe 5 points in the space corresponding to a different combination oftemperature, etchant flux, and plasma density. As mentioned, anexperimental design procedure such as DOE may be employed to select thesets of input parameters.

Once chosen, for each combination of input parameters, in operation 330an etch experiment is performed in order to measure an experimental etchprofile. (In some embodiments, multiple etch experiments are performedfor the same combination of values for the input parameters and theresulting etch profile measurements averaged together (possibly afterdiscarding outliers, etc.), for example.) This set of benchmarks is thenused for tuning and optimizing the model as follows: In operation 335 anetch profile is computed for each combination of values of the inputparameters, and in operation 340 an error metric is calculated which isindicative of (related to, quantifies, etc.) the difference between theexperimental and computed etch profiles over all the different sets ofvalues for the input parameters.

Note that this set of computed etch profiles (from which the errormetric is calculated) corresponds to a set of previously chosen modelparameters as specified in operation 310. A goal of the optimizationprocedure is to determine more effective choices for these modelparameters. Thus, in operation 350 it is determined whether thecurrently specified model parameters are such that the error metriccalculated in operation 340 is locally minimized (in terms of the spaceof model parameters), and if not, one or more values of the set of modelparameters are modified in operation 360, and then used to generate anew set of etch profiles—repeating operation 335 as schematicallyindicated in FIG. 3's flowchart—and thereafter a new error metric iscalculated in a repeating of operation 340. The process then proceedsagain to operation 350 where it is determined whether this newcombination of model parameters represents a local minimum over all thesets of input parameters as assessed by the error metric. If so, theoptimization procedure concludes, as indicated in the figure. If not,the model parameters are again modified in operation 360 and the cyclerepeats.

FIG. 4A presents a flowchart of a method 470 for refining modelparameters in an etch profile model. As depicted, method 470 begins bycollecting experimental etch profiles generated for a controlled seriesof etch chamber parameter sets. At a later stage, the method comparesthese experimentally generated etch profiles to theoretically generatedetch profiles produced using the etch profile model. By comparing theexperimentally and theoretically generated etch profiles, a set of modelparameters used by the etch profile model can be refined to improve themodel's ability to predict etch profiles.

In the depicted method, the process begins with an operation 472 wheresets of process parameters are selected for use in both thecomputational and experimental stages. These process parameters define arange of conditions over which the comparison is conducted. Each set ofprocess parameters represents a collection of settings for operating theetch chamber. As mentioned, examples of process parameters includechamber pressure, pedestal temperature, and other parameters that can beselected and/or measured within the etch chamber. Alternatively, or inaddition, each set of process parameters represents a condition of workpiece being etched (e.g., line width and line pitch formed throughetching).

After selecting the sets of process parameters for the experimental runs(note that a set of independent input parameters for the EPMoptimization will correspond to (and/or be computed from) each set ofprocess parameters), the experiments begin. This is depicted by a loopover multiple parameter sets and includes operations 474, 476, 478, and480. Operation 474 simply represents incrementing to the next processparameter set (Parameter Set(i)) for running a new experiment. Once theparameter set is updated, the method runs a new etch experiment (block476) using the parameters of the current parameter set. Next, the methodgenerates and saves an experimental etch profile (block 478) measured onthe work piece after the etch experiment runs with the current parameterset. The “generate and save etch profile” operation provides the etchprofile in a reduced dimensional space, as explained above, such as aprincipal components representation of the etch profile.

Each time a new process parameter set is used in an experiment, themethod determines whether there are any more parameter sets to consider,as illustrated at decision block 480. If there are additional parametersets, the next parameter set is initiated as illustrated at block 474.Ultimately, after all the initially defined process parameter sets areconsidered, decision block 480 determines that there are no more toconsider. At this point, the process is handed off to the modeloptimization portion of the process flow.

Initially in the model optimization portion of the flow, a set of modelparameters (Model Parameters(j)) is initiated as illustrated at block482. As explained, these model parameters are parameters that the modeluses to predict etch profiles. In the context of this process flow,these model parameters are modified to improve the predictive ability ofthe EPM. In some embodiments, the model parameters are reactionparameters representing one or more reactions to take place in the etchchamber. In one example, the model parameters are reaction rateconstants or the probabilities that a particular reactions will takeplace. Also, as explained elsewhere herein, the etch profile model mayemploy other parameters that remain fixed during the optimizationroutine. Examples of such parameters include physical parameters such asplasma conditions.

After the model parameters are initialized at operation 482, the methodenters an optimization loop where it generates theoretical etch profilescorresponding to each of the process parameter sets used to generate theexperimental etch profiles in the experimental loop. In other words, themethod uses the EPM to predict etch profiles which correspond to each ofthe process parameter sets (i.e., for all the different ParameterSet(i)'s). Note, however, that for each of these process parameter sets,what is actually input into the EPM (to run it) is a set of independentinput parameters which correspond to the given process parameters. Forsome parameters, an independent input parameter may be the same as aprocess parameter; but for some parameters, the independent inputparameter (actually fed into the EPM) may be derived/calculated from thephysical process parameter; thus they correspond to one another, butthey may not be the same. It should therefore be understood that in thecontext of this optimization loop in FIG. 4A (operations 482-496), theEPM is—to be very precise about it—run with respect to a set ofindependent input parameters corresponding to “Parameter Set(i)”,whereas in the experimental loop (operations 472-480) the experimentsare run with process parameters corresponding to “Parameter Set(i).”

In any event, initially in this loop, the method increments to a nextone of the parameter sets that were initially set in operation 472. Seeblock 484. With this selected parameter set, the method runs the etchprofile model using the current set of model parameters. See block 486.Thereafter, the method generates and saves the theoretical etch profilefor the current combination of a parameter set and model parameters(Parameter Set(i) and Model Parameter(j)). See block 488. The “generateand save etch profile” operation provides the etch profile in a reduceddimensional space such as a principal components representation of theetch profile.

Ultimately all the parameter sets are considered in this loop. Beforethat point, a decision block 490 determines that additional parametersets remain and returns control to block 484 where the parameter set isincremented to the next parameter set. The process of running the modeland generating a saving theoretical etch profiles repeats for each ofthe parameter sets (Parameter Set(i)).

When there are no remaining parameter sets to consider for the modelparameters currently under consideration (Model Parameters(j)), theprocess exits this loop and calculates an error between the theoreticaletch profile and the experimental etch profiles. See block 492. Incertain embodiments, the error is determined across all the ParameterSets(i) for the process parameters, not just one of them.

The method uses the error determined in block 492 to decide whether theoptimization routine for the model parameters has converged. See block494. As described below, various convergence criteria can be used.Assuming that the optimization routine has not converged, processcontrol is directed to a block 496 where the method generates a new setof model parameters (Model Parameter(j)) which could improve the model'spredictive ability. With the new set of model parameters, processcontrol returns to the loop defined by blocks 484, 486, 488, and 490.While in this loop, the Parameter Set(i) is incremented repeatedly andeach time the model runs to generate a new theoretical etch profile.After all parameter sets are considered, the error between thetheoretical and experimental etch profiles is again determined at block492 and the convergence criteria and is again applied at block 494.Assuming that the convergence criterion is not yet met, the methodgenerates yet another set of model parameters for testing in the mannerjust described. Ultimately, a set of model parameters is chosen thatmeets the convergence criterion. The process is then completed. In otherwords, the method depicted in FIG. 4 has produced a set of modelparameters that improve the predictive ability of the etch profilemodel.

A related procedure is depicted in FIG. 4B. As shown there, theexperimental and theoretical etch profiles are generated for differentsubstrate feature structures, rather than different process conditions.Otherwise the basic process flow is the same. In some implementations,both feature structures and process conditions are varied for theexperimental and theoretical operations.

The different features may include different “line” and “pitch”geometries. See FIG. 4B-1. Pitch refers to smallest unit cell width thatcovers the feature being etched that will be repeated many times. Linerefers to the total thickness between two adjacent sidewalls, assumingsymmetry. As an example, the method may run repeating geometries ofL50P100, L100P200, L100P300, L75 P150 etc. where numbers represent theline width and pitch in nanometers.

In the depicted embodiment, a process 471 begins by selecting fixed andvarying parameters (model parameters) of the etch profile model. Thesemay be physical and chemical reaction parameters in some embodiments.Additionally, the substrate features are selected. See operation 473.

For each feature geometry (incremented Feature Set(k) as illustrated inoperations 475 and 481), the method runs the etch process for using thecurrent feature geometry, generates the experimental etch profile(Experimental Etch Profile(k)), and saves the etch profile. Seeoperations 477 and 479. As before, each experimental etch profile issaved in a reduced dimensional representation.

Thereafter, the method initializes the model parameters (ModelParameters(j)) for tuning. See operation 483. For each feature geometry(incremented as Feature Set(k) in operations 485 and 491), the methodruns the etch profile model generates a theoretical etch profile(Theoretical Etch Profile(k)), and saves the etch profile. Seeoperations 487 and 489. As before, each theoretical etch profile issaved in a reduced dimensional representation.

For each set of Model Parameters(j) considered in the loop containingoperations 487 and 489, the method compares the theoretical andexperimental etch profiles to determine the error between the etchprofiles over all the substrate features sets. See operation 493. If theprocess has converged, as determined at operation 495, the process iscomplete and the current model parameters are selected. If the processhas not converged, the method generates a new set of Model Parameters(j)and returns again to the loop defined by operations 485, 487, 489, and491.

In some embodiments, a separate model parameter set is selected for eachfeature set. In such cases, the method may plot or otherwise determine arelationship between line/pitch ratio (or another characteristics of thefeatures) and the final converged model parameters. If the convergedmodel parameter values are reasonably constant, possibly with somenoise, the method use the average model parameter values for theimproved edge profile model. If the converged model parameter valuesexhibit a trend, the method may use polynomial fit do develop a functionthat may be used to select model parameter values for each feature set(e.g., line and pitch geometry).

As should be apparent, feature sets, process parameter sets, or othervariables are used to conduct multiple experiments and therefore producemultiple experimentally-determined etch profiles. In someimplementations, half or some other fraction of these etch profiles (andassociated parameter sets) are used for training, as illustrated in theabove flow charts, and the remaining etch profiles are used forvalidation. The training etch profiles generate tuned model parameters,which are used in the etch profile model and validated by applying thetuned model to predict etch profiles for the validation set. If theerror between experimental and theoretical etch profiles for thevalidation set is statistically higher than the error found atconvergence using the training set, a different training set is used totune the model as before.

Details Regarding Iterative Non-Linear Optimization Procedures

The model parameter optimization procedure just described in the contextof FIG. 3 is generally an iterative non-linear optimizationprocedure—e.g., it optimizes an error metric which is, in general, anon-linear function of the input parameters—and, as such, varioustechniques known in the art for non-linear optimization may be employed.See, for example: Biggs, M. C., “Constrained Minimization UsingRecursive Quadratic Programming,” Towards Global Optimization (L. C. W.Dixon and G. P. Szergo, eds.), North-Holland, pp 341-349, (1975); Conn,N. R., N. I. M. Gould, and Ph. L. Toint, “Trust-Region Methods,”MPS/SIAM Series on Optimization, SIAM and MPS (2000); Moré, J. J. and D.C. Sorensen, “Computing a Trust Region Step,” SIAM Journal on Scientificand Statistical Computing, Vol. 3, pp 553-572, (1983); Byrd, R. H., R.B. Schnabel, and G. A. Shultz, “Approximate Solution of the Trust RegionProblem by Minimization over Two-Dimensional Subspaces,” MathematicalProgramming, Vol. 40, pp 247-263 (1988); Dennis, J. E., Jr., “Nonlinearleast-squares,” State of the Art in Numerical Analysis ed. D. Jacobs,Academic Press, pp 269-312 (1977); Moré, J. J., “The Levenberg-MarquardtAlgorithm: Implementation and Theory,” Numerical Analysis, ed. G. A.Watson, Lecture Notes in Mathematics 630, Springer Verlag, pp 105-116(1977); Powell, M. J. D., “A Fast Algorithm for Nonlinearly ConstrainedOptimization Calculations,” Numerical Analysis, G. A. Watson ed.,Lecture Notes in Mathematics, Springer Verlag, Vol. 630 (1978); each ofwhich is hereby incorporated by reference in its entirety for allpurposes. In some embodiments, these techniques optimize an objectivefunction (here the error function/metric) subject to certain constraintswhich may be placed on the input parameters and/or the error metric. Incertain such embodiments, the constraint functions themselves may benon-linear.

For example, in embodiments where the computed etch profile isrepresented with a set of stacked trapezoids which are output by theEPM, the error metric may be defined as the difference between the arearepresented by the boundaries of these stacked trapezoids and the areaof the measured experimental etch profile. In this case, the errormetric is a non-linear function of the response variables output by theEPM, and thus a constrained optimization technique is selected fromthose just described (and/or from the incorporated references) whichallows for the specification of non-linear constraints. Note that in thecontext of the flowchart presented in FIG. 3, these various procedurescorrespond to how the one or more model parameters are modified inoperation 360, and also how one or more potential local minima in errorare detected and treated in operation 350.

In some embodiments, an iterative non-linear optimization procedurewhich is used to determine improved/tuned model parameters as shown inFIG. 3 may be divided into multiple phases, and in certain suchembodiments, the different optimization phases may correspond todifferent layers of material on the surface of the semiconductorsubstrate being etched. This approach may also reduce the computationalburden by reducing the number of input parameters being varied andsimplifies the error metric being calculated. For instance, if thesubstrate to be etched includes a multilayer stack of differentsequentially deposited materials, because the different layers, ingeneral, have different material compositions, in general, differentchemistries characterize the local etch process occurring in eachlayer—e.g., a different etch reaction (or reactions), different sidereactions, different reactions between by-products, or even if the same(or similar) chemical reactions are occurring, they may generally beoccurring at different rates, in different stoichiometric ratios, etc.Thus, in order to setup an etch profile model (EPM) corresponding to theetching of the whole multilayer stack, input parameters fed into themodel generally include different sets of parameters corresponding tothe different stacked layers. As described above, these sets may includeparameters indicating which chemical reactions are to be included in themodeling of the etch processes, as well as parameters characterizing thereactions themselves reaction probabilities, sticking coefficients, andthe like.

However, it is recognized that an optimization protocol does notnecessarily need to optimize every parameter simultaneously, e.g. somemay remain fixed in operation 360 of FIG. 3 while others are allowed to“float” and be modified in one or more particular cycles/rounds ofoptimization as schematically illustrated in the figure. Therefore,based on the observation that the chemical processes occurring in eachlayer are to a certain extent local to that layer, in some embodiments,optimization may be accelerated by tuning the model parametersassociated with one layer, individually, while holding the parametersassociated with the other layers fixed, and thereafter selecting anotherlayer, allowing its parameters to “float,” while holding those for theothers fixed, and so forth, until all layers have been individuallytuned. The layer-by-layer tuning process may then repeated multipletimes, each time cycling through all the layers, until a certain degreeof optimization is attained, and at this point, a full optimization overall layers may be performed—i.e., allowing the model parameters for allthe layers to be varied/“floated”—based on the recognition that the fulloptimization will converge more efficiently (and possibly to a betterlocal minimum in the error metric) with the parameters associated witheach layer having been individually optimized. Going one step further,the entire layer-by-layer procedure may be repeated to improve resultsfurther—i.e., performing layer-specific optimization by cycling throughthe layers one or more times, and then performing a global optimization,which allows the model parameters of all layers to float. Note that, inthe context of FIG. 3, the selection of certain model parameters andallowing them to “float” (and thus be individually optimized for aspecific layer) while others are held fixed, would be done as part ofthe parameter modification operation 360 of FIG. 3 (in these and similarclasses of embodiments).

As a specific example illustrating the foregoing individuallayer-by-layer optimization procedure, consider the case of modeling theetching of a layer underneath an etch mask, where both the etch masklayer and the layer beneath it are etched to some extent. This thusconstitutes a 2-layer etch model where the parameters for each of thetwo layers may be individually optimized prior to full simultaneousoptimization of the model parameters corresponding to both layers.

Therefore, one begins by specifying values for all the model parameters,running the model to generate computed etch profiles over all the setsof values of the input parameters—representing different experimentaletch conditions—and calculating an error metric indicative of thedifference between the experimental and computed etch profiles over allthe profiles corresponding to the multiple sets of values for theindependent input parameters. One may then proceed by selecting thelayer beneath the etch mask—say a layer of dielectric—for individuallayer-specific optimization, modifying one or more model parametersassociated with this (dielectric) layer for optimization, re-running themodel over all sets of values of the independent input parameters,calculating a new error metric, again modifying one or more modelparameters associated with the dielectric layer, re-running the model,recalculating the error, and so forth, until a local minimum in error isobtained with respect to the dielectric layer.

The model parameters for the dielectric layer are then held fixed atthese values, the model parameters of the etch mask layer are selectedfor individual optimization, one or more of their values (of the modelparameters of the etch mask layer) modified, the model re-run, the errorrecalculated, and so forth until a local minimum in error is achievedwith respect to the etch mask layer. At this point, a full optimizationover the model parameters of both layers may be performed, or in someembodiments, before doing that, one or more additional cycles ofindividual dielectric layer and mask layer optimization may be performedso that the full optimization is more effective (e.g., converges faster,or converges to a better resulting local minimum in the total errormetric).

It should also be understood, that in some cases, the foregoinglayer-by-layer optimization procedure doesn't necessarily have to berestricted to the tuning of only a single individual layer at one time.For instance, if one were modeling the etching of a 6-layer stack, onevariation of the foregoing layer-by-layer optimization procedure wouldbe to select pairs of layers for simultaneous tuning—i.e., floating themodel parameters corresponding to pairs of adjacent layerssimultaneously—and do this sequentially for the 3 pairs, possibly repeatthe 3-step cycle multiple times, before then performing the fullsimultaneous optimization over model parameters for all the layers; asbefore, optionally, repeating the entire layer-by-layer procedure (or,in this case, pairwise layer-by-layer procedure) until a local minimumin error over the entire stack is identified.

It is also possible that the numerical optimization procedure (whetherperformed on a layer-by-layer basis before full optimization, orperformed directly as a full optimization over all layers) may result inmultiple local minima in the etch profile metric depending on thestarting point of the optimization (i.e., depending on the initialvalues chosen for the model parameters), as well as other factors, andthus there may be many local minimum which the optimization procedurecould potentially identify as representing the improved (and/or optimalmodel). In the case of many local minima in error, many potential setsof model parameters may be eliminated from consideration by definingphysically realistic upper and lower boundaries for these modelparameters. In some embodiments, the foregoing numerical optimizationsmay be performed for a plurality of choices for starting points (initialvalues for the model parameters) in order to potentially identify aplurality of local minima, and thus a plurality of candidate sets ofmodel parameters, from which the most preferred may be chosen (possibly,in some embodiments, because it has the lowest computed error metric ofall the candidates which satisfy the foregoing mentioned physicallyrealistic upper and lower bounds).

Dimensionality Reduction and Principle Component Analysis

In some embodiments, an etch profile model outputs values at a largenumber grid/mesh points (cells) at each time step during the calculatedetch profile evolution. These values corresponding to each cell or gridpoint map out the shape of the calculated etch profile. Such an exampleof a grid/mesh of points representing a computed etch profile areillustrated in FIG. 1, where each grid/mesh point has a value indicatingwhether or not that region of space is occupied by the feature at thattime during the etch process. In some embodiments, the verticaldimension of the mesh representing an etch profile is at least about 5,or at least about 10, or at least about 20. Depending on the embodiment,a minimum value for the vertical distance between vertically adjacentmesh points may be chosen to be 1 Å and can be as large as a fewangstroms, such as 5 Å, or 10 Å, or even 20 Å.

In practice, one would like to choose the distance between adjacentmesh/grid points to be small enough to provide a reasonably accuratelyrepresentation of the shape of the feature as it evolves in time (whichlikely depends on the intricacy of the profile), but not much (or any)smaller than necessary to achieve this reasonable representation(because more grid points entail more compute time). The horizontalseparation (in the plane of the wafer) between adjacent mesh/grid pointswould be chosen based on the same considerations, but in generalhorizontal and vertical separation would be chosen to be the same (i.e.,a uniform grid) or roughly comparable. This does not mean the verticaland horizontal grid dimensions are necessarily the same, however,because the width of the feature being modeled is not necessarily thesame as the height of the feature which is being modeled. Thus, thehorizontal dimension (number of horizontal points spanning a givendirection, x-dimension in 2D, x- and y-dimensions in 3D), may depend onwhether just a sidewall of a feature is being modeled, whether theentire feature is being modeled (it's span from one profile edge toanother), whether multiple adjacent features are being modeled, etc.

As stated, the mesh of values which are output by the etch profile modelprovide an estimation of where, in physical space, the edge of thefeature profile is located at different vertical elevations. From thisinformation (from these values at the mesh points) one can compute afeature width at different elevations, or in another view, a horizontalcoordinate of the edge (relative to some baseline) for each elevation.This is illustrated in FIG. 2. This set of coordinates may then beviewed as a point in multi-dimensional space representing the particularfeature profile. This vector space may be an orthogonal space, or it maybe a non-orthogonal space, however a linear transformation may be madeof this representation to an orthogonal space. If so, then thetransformed point's coordinates are distances in relation to a set oforthogonal axes in that space. In any event, when “profile coordinates”are referred to in this document, this refers generally to anyappropriate (approximate) mathematical representation of the profileshape.

In any event, because the etch profile model may output a large numberof “profile coordinates” (hereinafter inclusive of a grid/mesh of pointsas just described) and the goal is to have these accurately match themeasured experimental etch profiles, reducing the error in the etchprofile model—iteratively reducing the error combined over the differentexperimental process conditions as described with respect to FIG. 3above—may be a computationally demanding task. For example, if a set ofm measured experimental etch profiles are to be matched point-by-pointto calculated etch profiles consisting of n profile coordinates, thenthis amounts to optimizing a model to fit a dataset m×n data points.

It turns out, however, that there are latent statistical correlations inthe etch profiles (whether measured or calculated) and that one may takeadvantage of these correlations to recast the optimization problem in aform which is far more numerically tractable. For instance, while a finegrid of profile coordinates may consist of many data points, from astatistical viewpoint, the values of certain combinations of thesecoordinates are correlated with one another. To give a trivial butillustrative example, vertically adjacent coordinates will tend to becorrelated with one another—simply because the width of an etchedfeature is not going to change too drastically over the short lengthscale associated with adjacent grid points as one moves up or down theprofile. More complicated examples of correlations between profilecoordinates relate to the types of profile shapes which may generally beachieved by varying certain combinations of process coordinates. Severalexamples are shown in FIG. 5. For instance, certain process parameters,alone or in combination with one another, may be adjusted to cause anetched profile to be bowed either inward or outward, as shown in FIG. 5,and the profile coordinates (or grid points) which map out this bowingof the profile are thus statistically correlated with one another.Likewise, as also shown in FIG. 5, etch profiles obtained throughadjustment of various process parameters, individually or incombination, may exhibit a downward or upward taper, and thus profilecoordinates may be correlated to the extent that varying one or moreprocess parameters tends to cause this tapering effect. Two otherexamples of underlying profile correlation structures are top taper andbottom taper, as also illustrated in FIG. 5. Again, these underlyingprofile structures are manifestations of the fact that variations inprocess parameters tend to cause changes in the overall shape of theprofile rather than having a local effect at certain spots on theprofile without affecting other spots. This is, of course, a consequenceof the underlying physics and chemistry associate with the etch process.

As mentioned, because of these underlying statistical correlations, theoptimization problem presented above (described with respect to theflowchart in FIG. 3) can be recast in a form which is more amenable toiterative optimization techniques. One way of doing this is to identifyseveral types of canonical profiles shapes, and express the measuredand/or computed etch profile in terms of these canonical shapes—such asby writing the total profile (at each profile coordinate) as a weightedaverage of the set of canonical profile shapes (at each profilecoordinate). I.e., a set of vectors represents the canonical profileshapes and the total profile may be approximately expressed as a linearcombination of these vectors. In this manner, one can take advantage ofthe underlying statistical correlations and model changes in thecoefficients/weights of the linear combination representing the profile,rather than model the changes in all the individual profile coordinates.For example, if one were to choose bow and taper (see FIG. 5) as thecanonical shapes, then the problem of modeling say m=100 profilecoordinates is reduced to modeling changes in the 2 coefficients for bowand taper in the linear combination—i.e., constituting a dimensionalityreduction from 100 to 2. Which canonical shapes are useful may depend onthe process/layer type. The depicted methods provide a numerical way ofextracting those shapes from either experimental data or from performingsimulations with EPMs.

For this strategy to be effective the canonical shapes must provide agood, albeit not exact, representation of the different profile shapesinvolved in the analysis. The more independent canonical shapes includedin the representation, the more accurate the representation will be (inthe vector space of the canonical shapes). Thus, the question becomeswhat canonical shapes to use, and how many to include, recognizing thatincluding more canonical shapes makes the analysis more accurate, but italso makes it more computationally expensive, and in the context ofiterative optimization, it may affect the ability of the optimization toconverge, or to converge as desirable a local minimum.

One way of doing this is to have process engineers identify a few typesof canonical profiles shapes which they observe, based on their pastexperience, to frequently occur in their etch experiments. The advantageof this approach is that it is simple. A potential disadvantage is thatit is ad hoc (being simply based on the experience and intuition of theprocess engineer) and that it does not provide any way of determiningwhen a sufficient number of profile shapes have been included in theanalysis. In practice, any canonical profile shape that a processengineer identifies will get included, but this may, of course, beinsufficient to provide an accurate representation. More importantly,this type of methodology will not identify new correlations in theprofile data which have not previously been identified, either becausein previous work the shape was not as pronounced, or because it is aresult of a new etch process with different underlying physical andchemical processes taking place.

Another approach is to base the dimensionality reduction procedure on astatistical methodology which can automatically identify the importantcanonical profile shapes as well as to provide an estimate of how manyshapes need to be included in order to provide a sufficiently accuraterepresentation. One data analysis technique for achieving this isprinciple component analysis (PCA), which makes use of the singularvalue decomposition (SVD), a matrix decomposition technique fromnumerical linear algebra. A description of the PCA technique and variousapplications may be found (for example) in: Jackson, J. E., “A User'sGuide to Principal Components,” John Wiley and Sons, p. 592. [2] (1991);Jolliffe, I. T., “Principal Component Analysis,” 2nd edition, Springer(2002); Krzanowski, W. J., “Principles of Multivariate Analysis: AUser's Perspective,” New York: Oxford University Press (1988); each ofwhich is hereby incorporated by reference in its entirety for allpurposes.

As described in the foregoing references, PCA takes as its input a setof vectors—in this case each vector being a series of n etch profilecoordinates representing a single profile—and returns a new set of northogonal vectors known as the principal components (PC) which may besorted so that PCs 1-i (where i≤n) constitute the “best” ith dimensionalsubspace for representing the input profile vectors; “best” meansstatistically optimal in the least squares sense—i.e. that theith-dimensional subspace of PCs determined from the PCA minimizes thecombined RMS error between each input vector and its linearrepresentation in the subspace of the selected PCs. Of course, the morePCs which are included, the larger the dimension of the subspace and thebetter the representation of the input profile data; however, because asubspace constructed via PCA is optimal, the expectation is that notmany PCs are required—and the amount of statistical variation in theunderlying data which is captured by adding an additional PC may beassessed through the singular values of the underlying SVD. Thus, byusing PCA to identify the canonical profile shapes which underlie adataset of etch profiles, once can construct a reduced-dimensionallinear model for representing the etch profiles, and do so in a fashionwhich is automatic (does not rely on the expertise of the processengineer) and has the ability to identify new correlations in theprofile data, and in a manner which provides a statistical estimate ofhow many shapes/dimensions are required to provide a goodrepresentation.

The result of the foregoing methodology is that a significantdimensionality reduction may be achieved without significantlycompromising statistical error and that the number of data pointsrequired for fitting in the numerical optimization procedure describedabove may be substantially reduced. It is also noted that there aredifferent viable strategies for implementing the dimensionality reducingPCA procedure within the optimization procedure presented in FIG. 3. Forinstance, in the context of the manner in which the error metric iscalculated in operation 340 of FIG. 3, one way to employ adimensionality reduction procedure is to project the computed andcorresponding experimental etch profiles, individually, onto areduced-dimensional subspace (which may be constructed via PCA), andthen to calculate the difference between the profiles as projected ontothe subspace. Another way is to take the differences between thecomputed and corresponding experimental etch profiles, project thedifferences onto a reduced dimensional subspace representative of thepotential differences between experimental and calculated etch profiles,and view the total error metric as the combined lengths of these vectorsin the difference-sub space.

It is additionally noted that PCA may also be used to dimensionallyreduce the number of independent variables in the space of independentinput parameters, providing a similar benefit to that just described. Insome embodiments, the dimensionality reduction procedure may be appliedto both the profile coordinate space and the input parameter space,simultaneously, such as, for example, by performing a PCA on theconcatenated vectors of input parameters and corresponding measured etchprofiles.

Applications of the Optimized Computerized Etch Model

The optimized computerized etch models disclosed herein may be useful insemiconductor processing workflows wherever a detailed assessment andcharacterization of an etch process is desirable. For instance, if a newetch process is being developed, the model may be used to determine etchprofile characteristics for many combinations of process parameterswithout having to go into the lab and perform each experimentindividually. In this way, the optimized etch profile models may enablequicker process development cycles, and in some embodiments maysignificantly reduce the amount of work required to fine tune a targetprofile.

Lithographic operations and mask development may also benefit greatlyfrom accurate etch profile modeling because estimating edge placementerror (EPE) is typically quite important in lithographic work, and anaccurate calculation of profile shape provides that information. In someembodiments, through rigorous physics-based EPE estimation, an optimizedEPM may be used to generate a pattern proximity-corrected (PPC) designlayout for photoresist in a much shorter timeframe than typicallyattends the semi-empirical trial and error process for patternproximity-correction (PPC) now in widespread use. Details are providedbelow.

The optimized models disclosed herein may also be useful for solving thereciprocal problem: where one desires a specific target etch profile andwants to discover one or more specific combinations of processparameters (or EPM input parameters) for achieving it. Again, this couldbe done by experimental trial and error, but an accurate modeling of theetch profile that results from a given set of process parameters (or EPMinput parameters) and conditions can replace the need forexperimentation, or at least do so in the initial phases of exploringthe process/input parameter space, until good candidates may beidentified for full experimental study. In some embodiments, it may bepossible to, in effect, numerically invert the model—i.e., iterativelylocate a set of parameters which generate a given etch profile—in afully automated fashion. Once again, dimensionality reduction of theetch profile coordinate space (via PCA), and projection of the desiredetch profile onto this space, may make this numerical inversion morefeasible.

In certain embodiments, an optimized EPM may be integrated with anetcher apparatus or into the infrastructure of a semiconductorfabrication facility which deploys one or more etcher apparatuses. Theoptimized EPM may be used to determine appropriate adjustments toprocess parameters to provide a desired etch profile or to understandthe effect of a change in process parameters on the etch profile. Thus,for instance, a system for processing semiconductor substrates within afabrication facility may include an etcher apparatus for etchingsemiconductor substrates whose operation is adjusted by a set ofindependent input parameters which are controlled by a controller whichimplements an optimized EPM. As describe below, a suitable controllerfor controlling the operation of the etcher apparatus typically includesa processor and a memory, the memory storing the optimized EPM, and theprocessor using the stored EPM to compute etched feature profiles for agiven set of values of a set of input process parameters. Aftercomputing a profile, in some embodiments, the controller may (inresponse to the shape of the computed profile) adjust the operation ofthe etcher apparatus by varying one or more values of the set ofindependent input parameters.

Generally, an etcher apparatus which may be used with the disclosedoptimized EPMs may be any sort of semiconductor processing apparatussuitable for etching semiconductor substrates by removing material fromtheir surface. In some embodiments, the etcher apparatus may constitutean inductively-coupled plasma (ICP) reactor; in some embodiments, it mayconstitute a capacitively-coupled plasma (CCP) reactor. Thus, an etcherapparatus for use with these disclosed optimized EPMs may have aprocessing chamber, a substrate holder for holding a substrate withinthe processing chamber, and a plasma generator for generating a plasmawithin the processing chamber. The apparatus may further include one ormore valve-controlled process gas inlets for flowing one or more processgases into the processing chamber, one or more gas outlets fluidicallyconnected to one or more vacuum pumps for evacuating gases from theprocessing chamber, etc. Further details concerning etcher apparatuses(also generally referred to as etch reactors, or plasma etch reactors,etc.) are provided below.

Optimization of the Etch Profile Models by Reflectance Spectra MatchingTechniques

The etch profile (EP) model (EPM) optimization techniques disclosedherein may also be performed in the reflectance spectral space, or areduced dimensional subspace (RDS) derived from the space of spectralreflectances. In other words, the EPM optimization is done by matchingcalculated reflectance spectra (generated with the EPM) toexperimentally measured reflectance spectra, each spectra representingthe intensity of electromagnetic radiation reflected from an etchedfeature on the substrate surface at a series of wavelengths. The set ofreflectance spectra used for the optimization (both the spectragenerated via EPM and measured experimentally) may also correspond to asequence of etch time steps (i.e., representing different time snapshotsof an etch process or processes). As discussed in detail above, EPMsgenerally compute a theoretical etch profile as it evolves in timeduring an etch process, and so by including reflectance spectra fromdifferent etch time step in the optimization, the optimized model isstatistically valid over the sequence of etch times used in theoptimization.

The spectral matching (SM) optimization procedure follows the generalEPM optimization framework described above, e.g., in reference to FIG.3, the difference being that the SM optimization operates in terms ofspectral reflectances instead of etch profile coordinates. To dothis—because the typical output of an EPM is a computed etch profilerepresented by a series of etch profile coordinates—one generatescomputed reflectance spectra by simulating the reflection ofelectromagnetic radiation (EM) off of said computed etch profile. Whatis known in the art as “rigorous coupled wave analysis” (RCWA)constitutes one computational process which may be used for thispurpose, but any suitable procedure for simulating the interaction of EMradiation with the substrate feature under consideration may beemployed.

In any event, with the ability to generate reflectance spectra from anEPM, a general procedure may be implemented for optimizing said EPM interms of spectral reflectances. This is now described with respect toFIG. 6 which presents a flowchart illustrating a set of operations 301for tuning and/or optimizing an etch profile model.

As above, and in some embodiments, such a tuned and/or optimized modelreduces—and in some cases substantially minimizes—a metric which isrelated to (indicative of, quantifies, etc.) the combined differencesbetween the etch profiles which are measured as a result of performingthe etch experiments, and the corresponding computed etch profiles asgenerated from the model. In other words, an improved model may reducethe combined error over the different experimental process conditions(as designated by the different sets of specified values of the selectedprocess parameters—which are used to compute independent inputparameters to the EPM).

As shown in FIG. 6, the reflectance spectra-based optimization procedure601 begins at operation 610 with the selection of a set of modelparameters to be optimized and the specification of their initialvalues—again, these model parameters may be chosen to be parameterswhich characterize the underlying chemical and physical processes(reaction probabilities, sticking coefficients, etc.), some or all ofthese will be adjusted based on the experimental data to improve themodel. The initial values may be those found in the literature, they maybe calculated based on other simulations, determined from experiment, orknown from previous optimization procedures, etc.

The model parameters chosen and initialized in operation 610 are thenoptimized over a set of independent input parameters, which are selectedand given multiple sets of values in operation 620. Such independentinput parameters may include, for example, parameters which characterizethe plasma in the reaction chamber: temperature, etchant flux, plasmadensity, etc. For each combination of values of independent inputparameters, in operation 630 an etch experiment is performed in order tomeasure an experimental etch reflectance spectra. (In some embodiments,multiple etch experiments are performed for the same combination ofvalues for the input parameters and the resulting reflectance spectrameasurements are averaged together (possibly after discarding outliers,noisy spectra, etc.), for example.) This set of benchmarks is then usedfor tuning and optimizing the model as follows: In operation 635 a setof computed reflectance spectra are generated—which correspond to themeasured spectra from operation 630 and thus are generated for eachcombination of values of the input parameters—by running the EP model toyield an etch profile, and then converting the computed etch profiles tospectral reflectances as described above (e.g., by using RCWA). At thispoint, there are corresponding experimental and computed reflectancespectra generated from each set of chosen values for the independentinput parameters, and thus suitable for comparison. The comparison isdone in operation 640, where an error metric is calculated which isindicative of (related to, quantifies, etc.) the difference between theexperimental and computed reflectance spectra over all the differentsets of values for the input parameters.

Analogously to what was described above with respect to FIG. 6, this setof computed etch profiles (from which the error metric is calculated)corresponds to a set of previously chosen model parameters as specifiedin operation 610. A goal of the optimization procedure is to determinemore effective choices for these model parameters. Thus, in operation650 it is determined whether the currently specified model parametersare such that the error metric calculated in operation 640 is locallyminimized (in terms of the space of model parameters), and if not, oneor more values of the set of model parameters are modified in operation660, and then used to generate a new set of reflectancespectra—repeating operation 635 as schematically indicated in FIG. 6'sflowchart—and thereafter a new error metric is calculated in a repeatingof operation 640. The process then proceeds again to operation 650 whereit is determined whether this new combination of model parametersrepresents a local minimum over all the sets of input parameters asassessed by the error metric. If so, the optimization procedureconcludes, as indicated in the figure. If not, the model parameters areagain modified in operation 660 and the cycle repeats.

If it is desired that the EPM be optimized (in the foregoing manner) foretch processes of different time durations, or be optimized forcomputing reflectance spectra at sequences of times over the course ofan etch process, a consideration is the extent to which the experimentalreflectance spectra used to optimize the EPM may be determinedaccurately from optical measurements over the course of an etch process.A related issues is the rate at which these measurements may beperformed over the course of the etch process.

Broadly, measurements of spectral reflectance may be performed in situor ex situ. Ex situ measurements are generally more accurate due toemployment of an external dedicated metrology tool (external to the etchchamber), but such measurements require that the wafer be removed fromthe etch chamber and thus that the etch process be stopped in order toutilize the tool. Since stopping and re-starting an etch process wouldlead to all sorts of systematic errors relative to an etch process ofcontinuous duration, accumulating reflectance spectra for a sequence ofdifferent etch times ex situ generally involves etching a sequence ofdifferent wafers each for a different desired duration and thenmeasuring reflectance form each individually. On the other hand, in situspectral reflectance measurements may be made continuously (orsubstantially continuously, or at least quite rapidly) withoutinterrupting the ongoing etch process, and thus a single wafer can beused to generate reflectance spectra corresponding to a sequence of etchtimes (which also eliminates (or at least reduces) the possibility ofwafer-to-wafer variation being interpreted as representing the etchtime-dependence of the reflectance spectra). However, wafer-to-wafervariation aside, for a variety of reasons, in situ spectral reflectancemeasurements tend to be less accurate than when a dedicated externalmetrology tool is used.

Although a spectral space EPM optimization may be done with respect toex situ or in situ measured spectral data, for instance, as alternativeembodiments, also disclosed herein are techniques for attaining (atleast to a certain extent) the advantages of both ex situ and in situspectral reflectance measurements without their respective drawbacks. Inparticular, the strategy is to use experimental reflectance spectra foroptimizing the EPM which have been generated from rapid in situ spectralreflectance (optical) measurements taken during ongoing etch processes(at the sequence of etch times desired to optimize the EPM) that arecalibrated using ex situ measurements taken with a dedicated metrologytool.

This may be done as follows. One or more wafers are etched for aduration covering the desired sequence of etch times, and throughout theongoing etch processes spectral reflectance optical measurements aretaken in situ. The measurement rate may be quite rapid, for example witha frequency of 1 Hz, 2 Hz, 5 Hz, 10, Hz, 15 Hz, 20 Hz, 50 Hz, or even100 Hz. In some embodiments, optical measurements taken at consecutiveetch times over at least a portion of the sequence of etch times areseparated by 0.01-1 second (i.e., with a frequency of 100 Hz to 1 Hz),or are separated by 0.05-0.5 second (i.e., with a frequency of 20 Hz to2 Hz). Separately, a set of wafers are etched for different specifiedetch durations, and after each etch process is concluded, and the wafersremoved from the processing chambers in which they were etched,reflectance spectra are optically measured ex situ with a dedicatedexternal metrology tool. The in situ measurements at the different etchtimes are then calibrated by comparing them to the ex situ measurementsof corresponding duration, and adjusting the in situ reflectance spectraintensities accordingly. These reflectance spectra, generated from insitu optical measurements calibrated with ex situ optical measurements,may then be used in the EPM optimization described with respect to FIG.3R.

The optimization procedure may also be performed with respect to areduced-dimensional subspace (RDS)—similar to what was done with respectto the etch profile space, but in this case, a dimensionality reductionof the spectral space—which involves using the RDS to calculate theerror metric which is minimized (usually locally, or approximately so)in the optimization. One way of constructing the RDS is by way of PCAwhereby, instead of doing the PCA in the space of etch profilecoordinates as was described above, the PCA may be done on the fullspace of spectral reflectances. In so doing, a significantdimensionality reduction of the spectral space may be achieved withoutsignificantly compromising the statistical error in the numericaloptimization. Here, the PCA may identify important canonical spectralshapes, and it also (as described above) provides an estimate of howmany shapes should be included to achieve some level of desiredstatistical accuracy. In this manner, as when done in the etch profilecoordinate space, the number of data points required for fitting in thenumerical optimization procedure may be significantly reduced, andconvergence of the numerical optimization achieved more rapidly.

Likewise, and similarly to the case of optimization in the etch profilecoordinate space, it is also noted that there are different viablestrategies for implementing the use of a RDS, e.g., within theoptimization procedure presented in FIG. 6, whether the RDS isconstructed via PCA, or PLS (as described below), or otherwise. Thus,for instance, in the context of the manner in which the error metric iscalculated in operation 640 of FIG. 6, one way to employ adimensionality reduction procedure is to project the computed andcorresponding experimental spectral reflectances, individually, onto theRDS, and then to calculate the difference between the reflectancespectra as projected onto the subspace. Another way is to take thedifferences between the computed and corresponding experimentalreflectance spectra, and then project the differences onto a reduceddimensional subspace representative of the potential differences betweenexperimental and calculated reflectance spectra; the total error metricis then viewed as the combined lengths of these vectors in thedifference-subspace (of reflectance spectra).

Rather than perform a PCA, another way to construct the RDS is simply toselect a particular set of spectral wavelengths and to consider these(selected wavelengths) as the basis set for the RDS. Doing this,projecting two reflectance spectra onto the RDS and calculating theirdifference (in the RDS) amounts to calculating the difference inintensity of the reflectance spectra at those particular wavelengthsand, for example, summing the differences, which would then make theerror metric a number proportional to the root mean square (RMS) error(over those wavelengths). Generalizing this, the error metric may begiven as a weighted sum of quantities monotonically related to themagnitude of the differences between corresponding experimental andcalculated reflectance spectra at the particular selected wavelengths.

Moreover, if the experimental and computed reflectance spectra to becompared in the optimization procedure correspond to a sequence ofdifferent etch times, then an additional criteria defining the RDS maybe the selection of these particular etch times. Thus, in suchembodiments, the RDS is determined based on a selection of particularspectral wavelengths and the identification of particular etch times atwhich the wavelengths are considered. Moreover, in certain suchembodiments, the different wavelengths and etch times may be weighteddifferently in the calculation of the error metric. Thus, for example,if the spectral data at certain etch times is more probative than thedata at other etch times, then (some of) the former may be weighted moreheavily (i.e., particular wavelengths at particular etch times may beset to be larger than (some of) the weights corresponding to the samewavelengths at other etch times). Additionally (or alternatively),different wavelengths of the reflectance spectra may be weighteddifferently in the analysis, even at the same etch times.

Another alternative for constructing the RDS is to perform a partialleast squares (PLS) analysis. The PLS analysis takes advantage of theprinciple that the (reflectance) spectral history of an etch profile asit evolves during an etch process is predictive of the etch profilelater in the etch process and/or at the conclusion of the etch process.An illustration is provided in FIG. 7A which shows 4 reflectance spectracorresponding to 4 sequential times during at etch process (t₀, t₁, t₂,and t_(EP) (′EP′ indicates feature's final etch profile)) as related toa feature (shown at the right in the figure) as the feature is etcheddownwards. From the figure, it is apparent that the reflectance spectrachanges as the feature's profile changes over the course of the etch,and thus a statistical model may be generated via a PLS analysis whichrelates the geometric coordinates of a feature etch profile at theconclusion of an etch process with various reflectance values ofparticular wavelengths at particular times earlier in the etch process.The PLS analysis may identify which spectral wavelengths and at whichtimes earlier in the etch processes are most predictive of the finaletch profile, and the model may also assess the sensitivity of the finaletch profile to these wavelengths and/or times. These spectralwavelengths at the particular times can then be designated as the basisset for the RDS with respect to which the EPM is optimized. Moreover,the PLS analysis's determination of the relative statisticalsignificance of these designated wavelengths at particular timesprovides a basis for weighting them more heavily in the numericaloptimization of the EPM, e.g., by defining the statistical weights inthe error metric.

Stating it another way, a PLS analysis of geometric etch profilecoordinates versus reflectance spectra from earlier in the etch processmay be used to identify the sensitive spectral regions over the courseof the etch process from which an effective RDS may be constructed, andthe relative statistical weights given to these identified wavelengthsat the identified prior etch process times may be used in thecalculation of an error metric with respect to which the EPM parameteroptimization is performed. It is noted that the use of such an RDS forthe EPM optimization will presumably be efficient because it is targetedat statistically significant regions of the spectral space (as afunction of etch time).

The foregoing PLS analysis and resulting PLS model (which provides astrategy for differentially weighting particular spectral wavelengths,etch times, etc.) will be more statistically robust if it is constructedfrom etch process data (sets of reflectance spectra and correspondingetch profile coordinates for different etch times) which are collectedover many different wafers subject to a range of etch process conditions(which may roughly correspond to the range of process conditions overwhich the model parameters of the EPM are to be optimized (using theRDS)). FIG. 7B schematically presents such a set of reflectance spectraldata collected over many wafers in the form of a 3-D data block wherethe 3 indices of the data block correspond to wafer number (i), spectralwavelength (j), and etch process time (k). This 3-D data block may be“unfolded,” as indicated in the figure, into a 2-D “X” data block ofsize K times J, with K being the number of time points and J being thenumber of wavelengths. (The stride of the concatenated data vector isthe number of wavelengths J.) These are the independent variables whichgo into the PLS analysis. The dependent variables for the PLS analysisare in the 2-D “Y” data block, as shown in the figure, which containsthe final N geometric etch profile coordinates for each of the 1 numberof wafers, as indicated in the figure. From this over-complete set oftraining data, the PLS analysis builds a regression model to predict thedependency of the final etch profile coordinates on the reflectancespectra data at intermediate times during the etch process.

Note that while such etch profile and spectral reflectance data (to beused as a training set for the PLS model) may be measured experimentallyby performing etch processes on a series different wafers (and measuringreflectance), such experimentation may be costly and time consuming.However, if one already possesses an EPM of sufficient accuracy—such asone optimized by the procedure described above—a more efficientprocedure may be to generate etch data sets using said EPM and to usethem for constructing/training the PLS model. In principle, acombination of both experimental and computer generated etch profile andspectral reflectance data could also be used.

In any event, the use of computer generated reflectance spectra forbuilding a PLS model suggests an iterative procedure whereby one uses a(potentially) un-optimized EPM to generate a training set of reflectancespectra for the PLS analysis, and the resulting PLS model may then beused to identify a RDS (with statistical weights) for returning to theinitial EPM and optimizing it. The new optimized EPM may then, in turn,be used to generate new sets of etch data to construct a new (andbetter) PLS model, which identifies a new RDS for use in furtheroptimizing the EPM, and so forth. The procedure may be continued in thismanner (back and forth between EPM optimization and PLS optimization)for some predetermined number of iterations, or until significantimprovement in the PLS and/or EP models is no longer found withsubsequent iterations. A variation is to begin with an EPM optimized byany of the optimization techniques described above (e.g., not involvingthe PLS procedure) and go from there. Another variation is to use a fewexperimentally measured etch process data sets to construct the initialPLS model independent of the EPM, and then proceed to identify the RDSfor optimizing the initial EPM. Other variations on these generalthemes, and combinations thereof, will be apparent to those of skill inthe art in view of the foregoing discussion.

This foregoing iterative approach is schematically illustrated in FIG.8. As shown in FIG. 8, a process 801 of generating an optimized PLSmodel begins with an operation 810 of receiving an initial set ofreflectance spectra and corresponding set of etch profiles, both ofwhich correspond to a sequence of etch process time durations. Thesequence of etch times could represent different times over the courseof an etch process, or the sequence of etch times could represent etchprocesses of different total etch time durations (in other words, etchprocesses performed to completion but for different total etch times ondifferent substrates). In any event, this initial training set ofreflectance spectra (corresponding to the sequence of etch times) couldhave been measured experimentally, generated with an un-optimized EPM,or generated using an EPM optimized by another procedure such as thosedescribed above (e.g., one not involving PLS). After receiving thetraining set, a PLS analysis is performed in operation 820 to generatean initial PLS model. The PLS model relates the coordinates of the etchprofiles (received in operation 810) to the reflectance spectra (alsoreceived in operation 810). In particular embodiments, the PLS analysisgenerates a regression model which expresses the dependency of the etchprofile coordinates at later etch times or even at the conclusion of theetch process on certain wavelengths of the reflectance spectra atparticular times earlier in the etch process, as described above, aswell as the statistical sensitivity of this dependence.

This initial PLS model may be accurate enough for some purposes, and ifthis is determined to be the case in operation 830, the optimizationprocess concludes. However, if in operation 830 the PLS model is deemedto not be of sufficient accuracy, the process 801 continues to operation840 where the current PLS model (as constructed in operation 820) isused to determine a (statistically significant) reduced dimensionalsubspace (RDS) along with statistical weights for defining an effectiveerror metric (as described above). The new statistically-weightedspectral error metric is then used in operation 850 to optimize an EPMmodel according (for example) to the EPM optimization proceduredescribed with respect to FIG. 6. Such a statistically-weighted errormetric may be used (in the optimization, e.g., of FIG. 6) to act as aneffectively gauge of the difference between EPM computed andcorresponding measured reflectance spectra in a spectral subspace (ofthe full spectral space) deemed to be statistically significant by thePLS procedure.

This EPM optimization procedure may use the same spectral data as usedin operation 820, or it may use different spectral data (but, again, itis optimized utilizing the new spectral error metric defined inoperation 840). In any event, once the EPM is optimized (in operation850) it may be used to generate a new (and perhaps very extensive) setof computed reflectance spectra. This is done by generating a set ofcomputed etch profiles in in operation 860 and then in operation 865using these computed etch profiles to generate a set of computedreflectance spectra (for example, by using RCWA as described above andindicated in the figure). These spectra may then be fed—as the spectraltraining set—back into operation 820 where a new PLS model is generatedbased on this new (perhaps quite extensive) training set. Thestatistical accuracy of the new PLS model is assessed in operation 830;and the cycle of operations (840, 850, 860, 865, 820, and 830) may becontinued in repetition until, in one of the repetitions of operation830, the PLS model is deemed to be of sufficient statistical accuracy.

It is noted that while this kind of PLS model is useful for optimizingan EPM model (via the identification of a “good” RDS) it is alsoindependently useful for etch endpoint detection procedures, such asthose described in a co-pending U.S. patent application Ser. No.15/059,073, filed Mar. 2, 2016, by Bailey III, et al. For instance, asdescribed above, the PLS model may be viewed as a statisticaldetermination of which spectral regions over the course of an etchprocess are more/most predictive of the final etch profile resultingfrom the etch process. As such, the construction of the PLS model iseffectively a sensitivity analysis which identifies which spectralregions may be monitored over the course of an etch process to determinewhen the feature profile has been etched sufficiently (i.e., forendpoint detection). It is therefore also noted that the optimization ofthe EPM model through the statistical weighting of the optimization infavor of those spectral regions (as a function of etch time) which areimportant in the PLS model, in addition to potentially leading to a moreefficient EPM optimization, has the benefit of enhancing the statisticalaccuracy of the PLS sensitivity analysis because the PLS model isthereby being constructed from etch profile data sets produced by an EPMmodel whose optimization was statistically weighted in favor of the sameregions of the spectral space (over the etch process) which are deemedin important by the PLS analysis.

Capacitively Coupled Plasma (CCP) Reactors for Use in Etch Operations

Capacitively coupled plasma (CCP) reactors are described in U.S. Pat.No. 8,552,334, filed Feb. 9, 2009 as U.S. patent application Ser. No.12/367,754, and titled “ADJUSTABLE GAP CAPACITIVELY COUPLED RF PLASMAREACTOR INCLUDING LATERAL BELLOWS AND NON-CONTACT PARTICLE SEAL,” and inU.S. patent application Ser. No. 14/539,121, filed Nov. 12, 2014, andtitled “ADJUSTMENT OF VUV EMISSION OF A PLASMA VIA COLLISIONAL RESONANTENERGY TRANSFER TO AN ENERGY ABSORBER GAS,” each of which is herebyincorporated by reference in its entirety for all purposes.

For instance, FIGS. 9A-9C illustrate an embodiment of an adjustable gapcapacitively coupled confined RF plasma reactor 900. As depicted, avacuum processing chamber 902 includes a chamber housing 904,surrounding an interior space housing a lower electrode 906. In an upperportion of the chamber 902 an upper electrode 908 is vertically spacedapart from the lower electrode 906. Planar surfaces of the upper andlower electrodes 908, 906 (configured to be used for plasma generation)are substantially parallel and orthogonal to the vertical directionbetween the electrodes. Preferably the upper and lower electrodes 908,906 are circular and coaxial with respect to a vertical axis. A lowersurface of the upper electrode 908 faces an upper surface of the lowerelectrode 906. The spaced apart facing electrode surfaces define anadjustable gap 910 there between. During plasma generation, the lowerelectrode 906 is supplied RF power by an RF power supply (match) 920. RFpower is supplied to the lower electrode 906 though an RF supply conduit922, an RF strap 924 and an RF power member 926. A grounding shield 936may surround the RF power member 926 to provide a more uniform RF fieldto the lower electrode 906. As described in U.S. Pat. Pub. No.2008/0171444 (which is hereby incorporated by reference in its entiretyfor all purposes), a wafer is inserted through wafer port 982 andsupported in the gap 910 on the lower electrode 906 for processing, aprocess gas is supplied to the gap 910 and excited into plasma state bythe RF power. The upper electrode 908 can be powered or grounded.

In the embodiment shown in FIGS. 9A-9C, the lower electrode 906 issupported on a lower electrode support plate 916. An insulator ring 914interposed between the lower electrode 906 and the lower electrodesupport plate 916 insulates the lower electrode 906 from the supportplate 916. An RF bias housing 930 supports the lower electrode 906 on anRF bias housing bowl 932. The bowl 932 is connected through an openingin a chamber wall plate 918 to a conduit support plate 938 by an arm 934of the RF bias housing 930. In a preferred embodiment, the RF biashousing bowl 932 and RF bias housing arm 934 are integrally formed asone component, however, the arm 934 and bowl 932 can also be twoseparate components bolted or joined together.

The RF bias housing arm 934 includes one or more hollow passages forpassing RF power and facilities, such as gas coolant, liquid coolant, RFenergy, cables for lift pin control, electrical monitoring and actuatingsignals from outside the vacuum chamber 902 to inside the vacuum chamber902 at a space on the backside of the lower electrode 906. The RF supplyconduit 922 is insulated from the RF bias housing arm 934, the RF biashousing arm 934 providing a return path for RF power to the RF powersupply 920. A facilities conduit 940 provides a passageway for facilitycomponents. Further details of the facility components are described inU.S. Pat. No. 5,948,704 and U.S. Pat. Pub. No. 2008/0171444 (both ofwhich are hereby incorporated by reference in their entirety for allpurposes) and are not shown here for simplicity of description. The gap910 is preferably surrounded by a confinement ring assembly (not shown),details of which can be found in U.S. Pat. Pub. No. 2007/0284045 (whichis hereby incorporated by reference in its entirety for all purposes).

The conduit support plate 938 is attached to an actuation mechanism 942.Details of an actuation mechanism are described in U.S. Pat. Pub. No.2008/0171444 (which is hereby incorporated by reference in its entiretyfor all purposes). The actuation mechanism 942, such as a servomechanical motor, stepper motor or the like is attached to a verticallinear bearing 944, for example, by a screw gear 946 such as a ballscrew and motor for rotating the ball screw. During operation to adjustthe size of the gap 910, the actuation mechanism 942 travels along thevertical linear bearing 944. FIG. 9A illustrates the arrangement whenthe actuation mechanism 942 is at a high position on the linear bearing944 resulting in a small gap 910 a. FIG. 9B illustrates the arrangementwhen the actuation mechanism 942 is at a mid-position on the linearbearing 944. As shown, the lower electrode 906, the RF bias housing 930,the conduit support plate 938, the RF power supply 920 have all movedlower with respect to the chamber housing 904 and the upper electrode908, resulting in a medium size gap 910 b.

FIG. 9C illustrates a large gap 910 c when the actuation mechanism 942is at a low position on the linear bearing. Preferably, the upper andlower electrodes 908, 906 remain co-axial during the gap adjustment andthe facing surfaces of the upper and lower electrodes across the gapremain parallel.

This embodiment allows the gap 910 between the lower and upperelectrodes 906, 908 in the CCP chamber 902 during multi-step etchprocesses to be adjusted, for example, in order to maintain uniform etchacross a large diameter substrate such as 300 mm wafers or flat paneldisplays. In particular, this embodiment pertains to a mechanicalarrangement to facilitate the linear motion necessary to provide theadjustable gap between lower and upper electrodes 906, 908.

FIG. 9A illustrates laterally deflected bellows 950 sealed at aproximate end to the conduit support plate 938 and at a distal end to astepped flange 928 of chamber wall plate 918. The inner diameter of thestepped flange defines an opening 912 in the chamber wall plate 918through which the RF bias housing arm 934 passes. The laterallydeflected bellows 950 provides a vacuum seal while allowing verticalmovement of the RF bias housing 930, conduit support plate 938 andactuation mechanism 942. The RF bias housing 930, conduit support plate938 and actuation mechanism 942 can be referred to as a cantileverassembly. Preferably, the RF power supply 920 moves with the cantileverassembly and can be attached to the conduit support plate 938. FIG. 9Bshows the bellows 950 in a neutral position when the cantilever assemblyis at a mid-position. FIG. 9C shows the bellows 950 laterally deflectedwhen the cantilever assembly is at a low position.

A labyrinth seal 948 provides a particle barrier between the bellows 950and the interior of the plasma processing chamber housing 904. A fixedshield 956 is immovably attached to the inside inner wall of the chamberhousing 904 at the chamber wall plate 918 so as to provide a labyrinthgroove 960 (slot) in which a movable shield plate 958 moves verticallyto accommodate vertical movement of the cantilever assembly. The outerportion of the movable shield plate 958 remains in the slot at allvertical positions of the lower electrode 906.

In the embodiment shown, the labyrinth seal 948 includes a fixed shield956 attached to an inner surface of the chamber wall plate 918 at aperiphery of the opening 912 in the chamber wall plate 918 defining alabyrinth groove 960. The movable shield plate 958 is attached andextends radially from the RF bias housing arm 934 where the arm 934passes through the opening 912 in the chamber wall plate 918. Themovable shield plate 958 extends into the labyrinth groove 960 whilespaced apart from the fixed shield 956 by a first gap and spaced apartfrom the interior surface of the chamber wall plate 918 by a second gapallowing the cantilevered assembly to move vertically. The labyrinthseal 948 blocks migration of particles spalled from the bellows 950 fromentering the vacuum chamber interior and blocks radicals from processgas plasma from migrating to the bellows 950 where the radicals can formdeposits which are subsequently spalled.

FIG. 9A shows the movable shield plate 958 at a higher position in thelabyrinth groove 960 above the RF bias housing arm 934 when thecantilevered assembly is in a high position (small gap 910 a). FIG. 9Cshows the movable shield plate 958 at a lower position in the labyrinthgroove 960 above the RF bias housing arm 934 when the cantileveredassembly is in a low position (large gap 910 c). FIG. 9B shows themovable shield plate 958 in a neutral or mid position within thelabyrinth groove 960 when the cantilevered assembly is in a mid position(medium gap 910 b). While the labyrinth seal 948 is shown as symmetricalabout the RF bias housing arm 934, in other embodiments the labyrinthseal 948 may be asymmetrical about the RF bias arm 934.

Inductively Coupled Plasma Reactors for Use in Etch Operations

Inductively coupled plasma (ICP) reactors are described in US Pat. Pub.No. 2014/0170853, filed Dec. 10, 2013, and titled “IMAGE REVERSAL WITHAHM GAP FILL FOR MULTIPLE PATTERNING,” and in U.S. patent applicationSer. No. 14/539,121, filed Nov. 12, 2014, and titled “ADJUSTMENT OF VUVEMISSION OF A PLASMA VIA COLLISIONAL RESONANT ENERGY TRANSFER TO ANENERGY ABSORBER GAS,” each of which is hereby incorporated by referencein its entirety for all purposes.

For instance, FIG. 10 schematically shows a cross-sectional view of aninductively coupled plasma etching apparatus 1000 appropriate forimplementing certain embodiments herein, an example of which is a Kiyo™reactor, produced by Lam Research Corp. of Fremont, Calif. Theinductively coupled plasma etching apparatus 1000 includes an overalletching chamber structurally defined by chamber walls 1001 and a window1011. The chamber walls 1001 may be fabricated from stainless steel oraluminum. The window 1011 may be fabricated from quartz or otherdielectric material. An optional internal plasma grid 1050 divides theoverall etching chamber into an upper sub-chamber 1002 and a lowersub-chamber 1003. In most embodiments, plasma grid 1050 may be removed,thereby utilizing a chamber space made of sub-chambers 1002 and 1003. Achuck 1017 is positioned within the lower sub-chamber 1003 near thebottom inner surface. The chuck 1017 is configured to receive and hold asemiconductor wafer 1019 upon which the etching process is performed.The chuck 1017 can be an electrostatic chuck for supporting the wafer1019 when present. In some embodiments, an edge ring (not shown)surrounds chuck 1017, and has an upper surface that is approximatelyplanar with a top surface of a wafer 1019, when present over chuck 1017.The chuck 1017 also includes electrostatic electrodes for chucking anddechucking the wafer. A filter and DC clamp power supply (not shown) maybe provided for this purpose. Other control systems for lifting thewafer 1019 off the chuck 1017 can also be provided. The chuck 1017 canbe electrically charged using an RF power supply 1023. The RF powersupply 1023 is connected to matching circuitry 1021 through a connection1027. The matching circuitry 1021 is connected to the chuck 1017 througha connection 1025. In this manner, the RF power supply 1023 is connectedto the chuck 1017.

Elements for plasma generation include a coil 1033 is positioned abovewindow 1011. The coil 1033 is fabricated from an electrically conductivematerial and includes at least one complete turn. The example of a coil1033 shown in FIG. 10 includes three turns. The cross-sections of coil1033 are shown with symbols, and coils having an “X” extend rotationallyinto the page, while coils having a “•” extend rotationally out of thepage. Elements for plasma generation also include an RF power supply1041 configured to supply RF power to the coil 1033. In general, the RFpower supply 1041 is connected to matching circuitry 1039 through aconnection 1045. The matching circuitry 1039 is connected to the coil1033 through a connection 1043. In this manner, the RF power supply 1041is connected to the coil 1033. An optional Faraday shield 1049 ispositioned between the coil 1033 and the window 1011. The Faraday shield1049 is maintained in a spaced apart relationship relative to the coil1033. The Faraday shield 1049 is disposed immediately above the window1011. The coil 1033, the Faraday shield 1049, and the window 1011 areeach configured to be substantially parallel to one another. The Faradayshield may prevent metal or other species from depositing on thedielectric window of the plasma chamber.

Process gases (e.g. helium, neon, etchant, etc.) may be flowed into theprocessing chamber through one or more main gas flow inlets 1060positioned in the upper chamber and/or through one or more side gas flowinlets 1070. Likewise, though not explicitly shown, similar gas flowinlets may be used to supply process gases to the capacitively coupledplasma processing chamber shown in FIGS. 6A-6C. A vacuum pump, e.g., aone or two stage mechanical dry pump and/or turbomolecular pump 1040,may be used to draw process gases out of the process chamber 1024 and tomaintain a pressure within the process chamber 1000. A valve-controlledconduit may be used to fluidically connect the vacuum pump to theprocessing chamber so as to selectively control application of thevacuum environment provided by the vacuum pump. This may be doneemploying a closed-loop-controlled flow restriction device, such as athrottle valve (not shown) or a pendulum valve (not shown), duringoperational plasma processing. Likewise, a vacuum pump and valvecontrolled fluidic connection to the capacitively coupled plasmaprocessing chamber in FIGS. 6A-6C may also be employed.

During operation of the apparatus, one or more process gases may besupplied through the gas flow inlets 1060 and/or 1070. In certainembodiments, process gas may be supplied only through the main gas flowinlet 1060, or only through the side gas flow inlet 1070. In some cases,the gas flow inlets shown in the figure may be replaced more complex gasflow inlets, one or more showerheads, for example. The Faraday shield1049 and/or optional grid 1050 may include internal channels and holesthat allow delivery of process gases to the chamber. Either or both ofFaraday shield 1049 and optional grid 1050 may serve as a showerhead fordelivery of process gases.

Radio frequency power is supplied from the RF power supply 1041 to thecoil 1033 to cause an RF current to flow through the coil 1033. The RFcurrent flowing through the coil 1033 generates an electromagnetic fieldabout the coil 1033. The electromagnetic field generates an inductivecurrent within the upper sub-chamber 1002. The physical and chemicalinteractions of various generated ions and radicals with the wafer 1019selectively etch features of the wafer.

If the plasma grid is used such that there is both an upper sub-chamber1002 and a lower sub-chamber 1003, the inductive current acts on the gaspresent in the upper sub-chamber 1002 to generate an electron-ion plasmain the upper sub-chamber 1002. The optional internal plasma grid 1050limits the amount of hot electrons in the lower sub-chamber 1003. Insome embodiments, the apparatus is designed and operated such that theplasma present in the lower sub-chamber 1003 is an ion-ion plasma.

Both the upper electron-ion plasma and the lower ion-ion plasma maycontain positive and negative ions, through the ion-ion plasma will havea greater ratio of negative ions to positive ions. Volatile etchingbyproducts may be removed from the lower-subchamber 1003 through port1022.

The chuck 1017 disclosed herein may operate at elevated temperaturesranging between about 10° C. and about 250° C. The temperature willdepend on the etching process operation and specific recipe. In someembodiments, the chamber 1001 may also operate at pressures in the rangeof between about 1 mTorr and about 95 mTorr. In certain embodiments, thepressure may be higher as disclosed above.

Chamber 1001 may be coupled to facilities (not shown) when installed ina clean room or a fabrication facility. Facilities include plumbing thatprovide processing gases, vacuum, temperature control, and environmentalparticle control. These facilities are coupled to chamber 1001, wheninstalled in the target fabrication facility. Additionally, chamber 1001may be coupled to a transfer chamber that allows robotics to transfersemiconductor wafers into and out of chamber 1001 using typicalautomation.

Also shown in FIG. 10 is system controller 1050. As described furtherbelow, such a system controller 1050 may control some or all of theoperations of an etcher apparatus, including adjustment of the etcher'soperation in response to the generation of a computed etch profile usingan optimized EMP as described herein.

Predictive Pattern Proximity-Correction of Mask Design Layouts

Extension of photolithography to the 20 nm node and beyond drivesadvanced resolution enhancement techniques that continue to impose eventighter tolerance requirements on photolithography and etch as well asmask design and manufacturing. Presence of residual errors in photomasksand the limitations involved in capturing those in process models havehelped drive correction of mask manufacturing effects. However, in theplasma-based etch process itself—after transfer of patterned photoresistthrough photolithography—long-range non-uniformities, such as patternloading of plasma flux, and short-range defects such as “proximitydefects” in the etching of the pattern defined by the photoresist,contribute to the observed defect signatures in the overall patternedetch process. A simple example is illustrated in FIG. 11A which shows across-sectional view of a 2-layer stack of material on a semiconductorsubstrate before and after a feature is etched into it, as defined by alayer of photoresist 1101 (atop the 2-layer stack). The figureillustrates that even in a relatively idealized etch process a “foot”1111 at the base of the transferred pattern of photoresist 1101 (asprojected by the mask (not shown)) may affect the width of the etchedfeature, and even aside from this, the figure shows that the sidewallsof the feature after being etched may have a slight taper to them,rather than being perfectly vertical. FIG. 11B shows a top-view of aprototypical feature—a trench having a 90 degree turn in it—andillustrates that the intended design of such a feature (FIG. 11B-1) maybe altered due to such proximity effects as shown in the fragmentedlayout (FIG. 11B-2). Such short-range proximity defects in the patternedetch process may act to increase intra-die critical dimension (CD)variability and contribute to degradation of integrated circuit (IC)performance and yield.

In the current state-of-the-art method for generating a photomask for apatterned etch process, remediation of pattern proximity defects (i.e.,“pattern proximity correction”) is addressed by either an empiricalrules-based correction strategy or an empirical model-based correctionstrategy. The rules-based procedure typically employs a reference maskwhich—when transferred via photolithography to form a referencephotoresist pattern layout on a test substrate and then etched—providesa standard set of offsets/corrections for a given pitch/CD associatedwith a standard set of line/space features in the reference layout. Sucha rules-based approach has limited accuracy when it comes to handlinggeneralized photoresist layouts.

The model-based approach utilizes what is commonly referred to as avariable etch bias model (VEB). Other similar heuristic models includewhat are known as compact litho-etch bias models (on the etch side) andcompact resist models (on the lithography side). While the approachitself is termed “model-based,” this refers only to astatistically-based least-squares fit “model” (as now brieflydescribed); it does not refer to a physics-based (i.e. chemical surfacekinetics based) computational model of the etch process (such as theoptimized etch profile models (EPM) described above which calculate theapproximate evolution of a feature's etch profile over time during theetch process).

In the standard empirical VEB approach, experimental CD information iscollected from a host of pre-printed mask test calibration patterns fora given set of process conditions. Notably, to do this, thesecalibration masks must be built, the associated calibration patterns ofphotoresist transferred (via a photolithography process using the builtmask) to actual wafer substrates, and then these (test) patterned wafersmust actually be etched under the given process conditions.

This, along with other steps, makes the entire VEB model-based approachquite time-consuming. The top portion of FIG. 12 shows the variousphases of the standard empirical VEB approach and illustrates a timeline(in units of weeks) for completion of the various phases, as well as forcompletion of the entire VEB-based mask build process. As illustrated inthe figure, the calibration mask build step of this process—i.e., thefirst of the steps just referred to—is typically preceded by a standardphotolithography (“Prolith”) simulation (Prolith is an industry-standardsoftware package available from KLA-Tencor Corporation of Milpitas,Calif.); and followed by an iterative optical proximity correction (OPC)step. In essence, these first two steps constitute a procedure fordetermining the mask which corresponds to a given photoresist patternlayout (which would be generated from an exposure to optical radiationprojected through the mask design). At this stage, the desired patternof photoresist is a calibration pattern, and thus the “calibration mask”is determined through this procedure and then a “build” is performed (asthe third step, as indicated in the figure).

Following the “Calibration Mask Build” (as indicated in the figure), aphotoresist pattern is transferred to a test substrate according to themask and the substrate is etched. CD information is then extracted fromtest structures and a least-squares fit of the data is performed (asindicated in the figure) which correlates CD bias with edge movements ofthe test structures. From this least-square fit model, edge correctionsare applied to the test mask build to recalibrate it and the mask buildprocedure is repeated. This mask-build/etch/least-squares-fit cycle isrepeated at least a few times prior to converging on printing the finalset of mask designs. (FIG. 12 is optimistic in this regard with respectto the VEB model as it only shows one or few of such build/etch/fitcycles.) In total, as shown in the figure, this state-of-the-artso-called “model-based” VEB approach is estimated to take at least 12weeks to complete; it can take, however, 16 weeks or more to complete(for example), if multiple build-etch-fit cycles are required. Moreover,since the procedure involves the experimental etching of real wafersubstrates, and both pre-etch and/or post-etch metrology of thesesubstrates, and moreover, over potentially many cycles, the entireprocess is (typically) also quite expensive from a materials- andresource-cost standpoint. Finally, limitations on this protocol'sstatistical accuracy should also be noted: A finite and limited numberof patterned sites on the test wafer's surface are measured and used inthe least-squares fitting procedure. Extrapolation outside of thisregression window will necessarily be of limited statistical validityand, of course, the real/production layout will have features which arenot reproduced or analogous to those found in the test calibrationpatterns.

In contrast to these almost totally empirical approaches, themethodology described herein uses a model-based approach employing areal physics and surface kinetics-based etch profile model (EPM)—i.e., amodel of the underlying physical processes and chemical reactionmechanisms occurring on the substrate surface and accounting for theplasma etch of the substrate; as described above, the EPM model tracksthe evolution of an etch profile on the semiconductor substrate as itevolves over the course of a plasma-based etch process. In the case of apatterned etch process, the time-evolution of the feature profile wouldproceed based on the patterning of some layer of photoresist (createdfrom a given mask layout) overlaid on a given material stack on thesurface of the semiconductor substrate.

Briefly, in the physics/chemistry model-based approach disclosed herein,for a given mask-open process, a target calibration pattern/layout (thatwould include, e.g., linear 2D line/pitch gratings, and might alsoinclude simple 3D patterns) is used to optimize a rigorous physics-basedEPM (such as described above). Metrology is performed on experimentalwafers with the targeted calibration pattern (after transfer viaphotolithography to a given material stack and etched), and the EPM iscalibrated to this experimental metrology using any of the variousoptimization procedures such as those described above. In someembodiments, the optimization may be performed using a cloud-based orcluster-based implementation, and the computation may involve generatinga large number of samples around a center point, followed by a search inthat parameter space for improved calibration/optimization of the EPMwith respect to the experimental data.

Once an optimized EPM is established (especially for a given etchprocess and substrate material stack), it may then be used in theimplementation of a computational predictive pattern-proximitycorrection (PPC) scheme which, in some embodiments, requires no furtherphysical experimentation. Thus, as shown in the lower portion of FIG.12, in using such a physics-based model approach, the methodology mayreduce the total mask build time by at least 3-4 weeks and will involvejust one final physical mask build step.

A basic overview of the PPC prescription is schematically illustrated inFIG. 11B with respect generally to an isolated feature—which would be asmall portion of an overall design layout. As shown in FIG. 11B-1, aninitial (trial) etch design layout (to be embodied in a layer ofphotoresist generated via photolithography by projecting through anappropriately designed optical mask) corresponding to the intendedetched design is received. In this case it is a simple L-shaped trench(it has a 90 degree bend). The edges of the received design layout(again, this is the intended design pattern) are then discretized—a setof points are selected in the horizontal plane of the etch designlayout—see the “fragmented layout” in FIG. 11B-2—and anoptimized/calibrated EPM model (such as that just described, optimizedaccording to a calibration pattern) is run over the selected set ofdiscretized edge points. The output from the EPM is the feature'scross-sectional profile (as shown in FIG. 1) as it evolves over timeduring simulated etch, computed with respect to the various discretizededge points. Run through to the final etch time, the EPM thus providesan estimate of the feature's edge placement error (EPE) around thecontours of the feature—see the “simulated contour” in FIG.11B-2—according to the fineness (or coarseness) of the discretization.The simulated contour shown in FIG. 11B-2 illustrates the proximitydefects likely to be found if one were to actually do a real plasma-etchusing the original photoresist pattern shown in FIG. 11B-1. Based on theEPM computation, however, the initial design layout may be modified, asshown in FIG. 11B-3, to provide a proximity-corrected design layoutwhich compensates for the expected defects. Transferring a layer ofphotoresist to the substrate and patterning it so that it resembles thisproximity-corrected (PPC) design layout, and then etching the substratewith this PPC will result in the “final pattern” shown in FIG. 11B-4,which illustrates the edges of the etched feature now more closelyaligning with the original intended design layout.

Based on this general prescription, a variety of approaches may beenvisioned. One might envision a brute-force approach where the entirepatterned surface of a wafer substrate is discretized with a largenumber of edge points and the calibrated EPM is run for each of the edgepoints to determine the appropriate proximity corrections. This may workin principle. In practice, the number of EPM calculations required tocover such a large grid of points would be quite expensive from acomputational perspective, and likely quite impractical.

Another approach, however, arises from the realization that there islikely to be a great deal of similarity between the actual physical andchemical processes occurring at different points on the wafer's surface,and within the different features being etched on the wafer's surface.Different feature geometries from the design layout coupled withvariations in plasma flux within the etch chamber will, of course, leadto certain differences, but there are likely to be significantsimilarities across the wafer—the same chemistries are involved, thesame plasma is involved, many features will have similar shapes, or fallinto different general classes of shapes, etc. Thus, with thisrealization, what is sought is a concrete procedure for takingadvantages of these similarities and avoiding the brute force EPMcomputation for every edge in a given design layout. Doing so providesan opportunity for enormous computational cost savings: there is no needto re-run an EPM for every feature in a large complicated photoresistdesign layout, because many points in the design are likely to yield thesame result. The key is figuring out what points these are.

The approach described herein for accomplishing this takes advantage ofthe idea that the etch reaction rates inside a feature are likely to bevery strongly correlated with the physical characteristics of the plasmawithin a feature as it is etched, or more generally, of any etchant orpassivation species within the feature during the etch process.Particularly, this is so because the material composition of eachfeature (i.e., the material stack on the semiconductor substrate) istypically going to be the same. In other words, if it is known (via theoptimized EPM) what is going to happen within one feature for a givenetchant (e.g., plasma-based) flux within the feature—e.g., how an edgeof the feature moves as it is etched—then in all likelihood the sameresult is going to occur in all features having the same in-featureplasma/etchant flux (IFPF) during the etch (or, at least, for featuresthat are have some gross geometric similarity).

To implement this idea—and to avoid the brute force EPM computation forevery edge—a set of targeted calibration structures is assembled. FIG.13A provides an illustration of a simple calibration pattern 1300 withcertain structures/features 1301 and 1302 selected from it. For eachtargeted calibration structure/feature, one or more characteristics ofan in-feature plasma flux (IFPF) is determined, and the optimized EPMmodel run for that calibration structure/feature to determine the timeevolution of the feature during the etch, and more particularly thefeature's edge placement error (EPE) as a result of the etch. If thetargeted calibration structures/features exhibit a range of IFPFcovering the range of IFPF likely to be seen in a real photoresistdesign layout, then this procedure of running the EPM over a limitednumber of calibration structures has nevertheless provided anapproximate mapping between IFPF and EPE. The mapping is referred toherein as a reduced order model or ROM and, as described herein, themapping may be conveniently represented in a look-up table (LUT) format,such as displayed in FIGS. 13B and 13C. Such a ROM LUT then constitutesa very fast computational tool around which a protocol may be developedfor proximity correction. It should, however, be understood that othercomputationally-efficient implementations may also be used to representthe ROM relationship. For instance, as described in more detail below, amachine learning model may be trained with a dataset similar to thatwhich may be used to construct a LUT (or perhaps the training datasetmay be even more comprehensive—see below). Although a LUT represents onecomputationally efficient/feasible implementation of the ROMrelationship between EPE and quantities characteristic of IFPF, otherimplementations may be even faster and/or provide better interpolationbetween points in the training set, and thus may be preferred, dependingon the embodiment. As explained, the concept of a LUT may be generalizedto include other relationships between IFPF related characteristics(e.g., IFPIF, IFPNF, IFPDF, etch time, etch depth, and edge shape) andEPE. Examples of such relationships include regression models, neuralnetworks, classification trees (e.g., random forests models), and thelike. The concept of a LUT may be viewed as including any of these.

In any event, referring again to the look-up table (LUT) embodiment ofwhat is more generally a reduced order model (ROM) of the masked etchprocess: As shown in FIG. 13B, each entry in the look-up table typicallyhas fields for one or more values of quantities which are characteristicof the IFPF—in this example, columns/fields for in-feature plasma ionand neutral fluxes, and passivant deposition flux (Γ*)—and a field forthe resulting EPE (in this example, labeled “Δx_(EPE)”) (or a quantitycharacteristic/indicative of EPE) that is expected to be associated withsaid IFPF-related quantities (as previously determined by running an EPMover the calibration structures). As indicated in the table entry ofFIG. 13B, the in-feature plasma ion flux (IFPIF), in-feature plasmaneutral flux (IFPNF), and in-feature passivant deposition flux (IFPDF)represent outputs of a compact physical model (CPM) of the in-featureplasma etchant species and which are generally determined bycalculations which take into account the effects of flux loading justabove the substrate, as well as accounting for the “visibility” atvarious depths inside the feature. (As further indicated in the LUTexample of FIG. 13B, flux “loading” is more important for determiningneutral and passivant species flux, whereas “visibility” relates to ionspecies flux, plasma ion flux being directional due to electromagneticfields within the processing chamber and hence very susceptible toshadowing effects from a feature's sidewalls.)

In addition, the different entries in the look-up table may correspondto a single total etch time or different entries may correspond todifferent etch times. In the table entry of FIG. 13B, a “Layer Depth”field (z₁, z₂, . . . z_(N)) is used instead of an “Etch Time” field (t₁,t₂, . . . t_(N)), for example, but the principle is the same: totabulate values for different intermediate times during the etch. (Thebenefit of assembling EPE data for multiple intermediate times duringthe etch is described in greater detail below.)

To make this more concrete, a simple illustration is provided in FIGS.14A and 14B which display a feature/structure of a semiconductorsubstrate labeled with the quantities held in the fields of the look-uptable. Both figures show cross-sectional profiles of two lines ofphotoresist from a photoresist layer, labeled L₁ and L₂, which define astructure/feature 1410 having width ‘w’ and pitch ‘P’ which is etched inan etch process. FIG. 14A shows schematically what may be viewed as thetrue profile of the feature at various etch times t₁ at which thefeature will have a corresponding depth z_(i)—this then represents thediscretization in time, or equivalently depth, as tabulated in thelook-up table illustrated in FIG. 13B. (As mentioned above, there iscorrespondence between etch time and etch depth.) FIG. 14B shows a“digital”/discretized representation of the same feature at thedifferent points during the etch, and how the EPE, AXEpE, is to becalculated, which is also tabulated in the look-up table of FIG. 13B.

To use the reduced order model (ROM) look-up table (LUT) to determine anEPE for a particular edge in a design layout, one thus uses a set of oneor more estimated values of quantities which are characteristic of theIFPF corresponding to the feature with which the edge is associated, andlooks up these quantities in the table. Thus, for instance, as shown inthe ROM LUT of FIG. 13B, one may use in-feature plasma ion flux (IFPIF),in-feature plasma neutral flux (IFPNF) (which includes plasmafree-radical species), and in-feature passivant deposition flux (IFPDF)as quantities characteristic of in-feature plasma flux (IFPF) forindexing into the LUT to obtain an estimate of the edge placement error(EPE) approximately corresponding to these quantities.

However these are not the only possible quantities which may representthe characteristics of the plasma within the feature as calculated by a“compact physical model” (CPM). In this respect, the phrase “quantity(or quantities) characteristic of IFPF” is intended (as used herein) toencompass the actual physical characteristics of the plasma/etchantwithin the feature (i.e., between its sidewalls) as determined from acomputational model (although, in principle, they could also bedetermined experimentally). However, IFPF is also intended (as usedherein) to encompass, more generally, other plasma/etchant parameterswhich although perhaps not representing the actual physicalcharacteristics of the plasma/etchant within the feature per se, theyare nevertheless strongly correlated with them.

An example is shown in the ROM LUT entry of FIG. 13C. In this ROM LUT,there are explicit fields for “Loaded Fluxes” (referring to the loadedfluxes above the feature) and a field for “Visibility” (representing theshadowing effects of a feature's sidewalls, obtained, for example, byhemi spherically averaging/integrating a feature's angularly-dependent“visibility kernel”—see additional details below). While these are not,strictly speaking, actual physical characteristics of the actual plasmaspecies within the feature (i.e., down inside it, between itssidewalls), taken together, these parameters are strongly correlatedwith the actual physical characteristics of the plasma within thefeature. For instance, if one knows the loaded fluxes above thesubstrate surface as well as a feature's approximate visibility (asthose technical phrases are understood in the art) then one maycalculate (e.g., via a CPM) the ion and neutral/radical plasma fluxdensities within the feature to good accuracy. Because of this, takentogether, such a set of features may also be said to constitute theactual in-feature ion and neutral/radical plasma fluxes which will leadto the EPE listed in the table. Hence, fields in the LUT like those ofFIG. 13C are also classified herein as “quantities characteristic of theIFPF.”

It is also noted that the LUT entries shown in FIGS. 13B and 13C containan “Edge” field. As a shortcut, instead of, for example, using loadedfluxes or visibility as keys into the look-up table, one may insteadlook up an edge in the look-up table directly. Typically, the edge fieldwould contain some sort of edge shape indicator whereby edges offeatures present in the design layout having geometric similarity toedges of features present in the calibration pattern may be identifiedand found in the look-up table. Thus, in some embodiments, an edge shapeindictor for the edge of a feature in the design layout may bedetermined by pattern matching the shape of said feature against theshapes of the features present in the calibration pattern (and then usedas a key into the look-up table). Because feature shapes are likely tobe strongly correlated with IFPF, doing this may make the edge shapeindicator a quantity characteristic of IFPF for purposes of indexinginto the LUT. In some embodiments, the look-up table may be searchedfirst based on the feature's determined edge shape indicator. In certainsuch embodiments, such a search based on the edge shape indicator may beused initially to narrow down relevant entries in the look-up tablebefore a detailed search (and/or interpolation) based on the otherquantities listed in the table is performed (such as a subsequent searchbased on IFPIF and/or INPNF).

Conceptually, the look-up table thus provides a very fast mappingbetween IFPF-related quantities and the EPE (edge placement error) of afeature as it is etched—given the process conditions and particularmaterial stack used to construct the look-up table. It is referred toherein as a reduced order model (ROM), not only because it is fast, butalso because it serves to reduce what amounts to a very complexphysical/chemical etch process down to a core causal relationshipbetween characteristics of local plasma flux (IFPF) (or flux ofnon-plasma-based etchant if that is the relevant etch process) and edgeplacement error (EPE). Once again, this ROM relationship (embodied inthe look-up table or similar construct) could be constructed using aphysics-based EPM calibrated using any of the optimization methodsdescribed in detail above. However constructed, once this relationshipis established, a prescription may be designed for doing patternproximity correction (PPC) of an initial/trial design layout forphotoresist based on the physics and chemistry of the etch processembodied in the ROM look-up table.

Such a set of operations are displayed in the flowchart of FIG. 15. Asshown in the figure, a method for generating a proximity-correcteddesign layout for photoresist to be used in an etch operation beginswith an operation 1510 of receiving an initial design layout, afterwhich, in operation 1520, a feature is identified in the design layoutfor proximity correction. Of course, in many cases, one will want tochoose a multitude of features in the design layout for proximitycorrection; more on this below. In any event, with regards to thisidentified feature, in operation 1540, the method proceeds by estimatingone or more quantities characteristic of an in-feature plasma flux(IFPF) within the feature at a time t during the modeled plasma-basedetch process, and then, in operation 1550, these one or more estimatedIFPF-related quantities are used to estimate an edge placement error(EPE) of an edge of the feature at time t using a reduced order model(ROM) embodied in the look-up table. (The quantities characteristic ofIFPF at time t serve as keys into the ROM look-up table.) Again, the ROMlook-up table which associates values of EPE at time t with one or morequantities characteristic of the IFPF, and it was constructed by runninga computerized etch profile model (EPM) under the set of processconditions at least to time t on a calibration pattern of photoresistoverlaid on the material stack. With the estimated EPE associated withthe feature determined, the method concludes with operation 1590 ofmodifying the initial design layout based on at the EPE.

The modified design layout may then serve as the finalproximity-corrected design layout for photoresist from which an etchphotomask design may be generated, for example, by using anindustry-standard software package such as “Prolith” mentioned above. Anactual photomask may then be physically formed, and a photolithographyoperation performed using it, in the usual fashion, to transfer a layerof photoresist to the substrate surface, which now will match theproximity-corrected design layout. Finally, the actual plasma-etchoperation may be performed.

As stated, in most cases, it is desired that pattern proximitycorrection (PPC) be done for many features in the initial design layout.Accordingly, FIG. 16 presents a method 1502 which is analogous to thatshown in FIG. 15, but involves pattern proximity correction with respectto multiple features (whose patterns are in the initial design layout).As shown in FIG. 16, method 1502 proceeds analogously to method 1501from FIG. 15, but after an operation 1550 where an EPE is estimated forthe first feature under consideration, it is determined in an operation1571 whether another feature should be considered. If so, the methodloops back to operation 1520 where another feature in the initial designlayout is selected, and the method proceeds as before, but with respectto the newly additionally considered feature to arrive at an estimate ofits EPE, again, in operation 1550. The method 1502 may then continue toloop according to the decision logic in operation 1571 until it isdetermined that no more features are to be considered, at which pointthe method proceeds to operation 1590 where the initial design is thenmodified based on the different EPEs estimated for all the differentfeatures which were considered.

As described above, various quantities relating to (characteristics of)the IFPF may be used as keys for indexing into the ROM LUT and therebyobtaining an estimate of the EPE. In the embodiment depicted in FIG.13C, a representation of plasma flux (e.g., as calculated by a CPM) hasbeen utilized in terms of above-wafer loaded plasma fluxes andin-feature visibility. In the embodiment depicted in FIG. 13B, the ROMLUT implements use of the CPM in terms of in-feature plasma ion flux(IFPIF), in-feature plasma neutral flux (IFPNF) (which includes plasmafree-radical species), and in-feature passivant deposition flux (IFPDF)as detailed above.

In addition, while most of the examples explained herein concern thecase of modeling a plasma-based etch process with a ROM LUT approach, insome embodiments, other etch processes may also be modeled effectivelywithin the framework of a LUT. For example, if there is no plasma, then,more generally, one or more quantities characteristic of an in-featureetchant flux/concentration (IFEF) could be used as keys for indexinginto a LUT which holds values of EPE corresponding to thisnon-plasma-based etch process.

Note that the process conditions set for the processing chamber, chambergeometry, etc. determine the “global plasma flux” (or more generally“global etchant flux”) far from the surface of the substrate—i.e., theprocess conditions dictate what “global plasma flux” would generallyexist in the processing chamber were there no substrate present. Ifthere is a substrate present, then the substrate affects the plasma fluxdirectly above it, in its vicinity—i.e., the loaded plasma flux isrelated to, and may be estimated based on, the global plasma flux asdetermined from the process conditions, but the they are not in, ingeneral, the same. In particular, the loaded plasma flux has ahorizontal radial dependence due to the presence of the substrate in thechamber; moreover, the radial dependence may be affected by the patterndensity of photoresist on the wafer surface corresponding to a givendesign layout. Thus the loaded plasma fluxes—loaded plasma neutral flux(LPNF) and/or loaded passivant deposition flux (LPDF)—may be estimatedbased on the global plasma flux (as determined by the chamberconditions) in conjunction with the design layout planned for the etchprocess. Note that it is not as important that one calculate loadingsfor plasma ion fluxes (PIF) because flux density/densities for ionicspecies generally do not deviate significantly from their “global plasmaflux” values. Thus, it will oftentimes be the case that the PIF valuestabulated in the ROM LUT will be unloaded plasma fluxes (but also notethat this does not necessarily have to be the case for all embodiments,and there may be some ionic species whose corrections for flux loadingare significant enough to warrant taking into account).

The ROM look-up table entry in FIG. 13C also has a field for in-featurevisibility. As indicated above, the visibility specifies the degree ofshadowing effects a feature's sidewalls have on plasma density due totheir blocking of directional ion flux. This is illustrated by thecross-sectional view of the feature shown in FIG. 17: lines-of-sight1710 and 1720 converge to a spatial point 1730 within thefeature—representing a particular depth at one of the edges—anddelineate the angular limits of that point's visible exposure todirectional ion flux; lines-of-sight 1710 and 1720 thus determine thefraction of directional ion flux that spatial point 1730 is subjected toduring the etch. More precisely, the ion flux for a particular ion at aparticular depth within a feature is given by angular integration (e.g.,done numerically) of a visibility kernel corresponding to that specificdepth within the feature (at a specific depth, the visibility kernel hasan angular dependence, for example, see lines of sight 1710 and 1720 inFIG. 17) with the ion energy angular distribution function (IEADF)associated with that particular ion of interest. (The IEADF comes fromthe global plasma model.) Thus, the visibility is closely related to ionflux density and so may be said to be a characteristic of IFPF as statedabove. For a given edge, the visibility kernel may be integrated so asto obtain an average/mean visibility value which may be tabulated forall the different edge depths (and/or etch times) present in the ROMlook-up table as shown in FIG. 13C. One may then simply use theintegrated visibility (associated with a feature of interest) to indexinto the ROM. In other embodiments, the product of the visibility kerneland the IEADF is integrated (over angle) to obtain the IFPIF which canthen be used as an index into the LUT as shown in FIG. 13B.

As illustrated in FIG. 17, a feature's “visibility” is primarilydetermined by its shape. However, the shape of a feature evolves overthe course of an etch process, and so there is a question as to whatshould be taken as the estimated shape of the feature during the etchprocess for purposes of determining a visibility corresponding to itwhich may then be used to index/key into the ROM LUT. A variety ofapproaches may be employed for this.

One approach is simply to assume that the estimated shape of the featurein question has an opening which corresponds to the given initial designlayout of photoresist and that the feature has substantially verticalsidewalls extending downward from the edges of its opening. In otherwords, that the feature has zero EPE for purposes of using thevisibility/flux-loading CPM picture as a way to index into the ROM LUT.In some embodiments, this approximation may be good enough.

A more sophisticated way of estimating feature shape and thus visibilityfor purposes of indexing into the LUT is illustrated by the flowchart inFIG. 18. FIG. 18 illustrates a pattern proximity-correction (PPC) method1503 that begins similarly to method 1502 of FIG. 16, but afteroperation 1520 (feature selection), the method proceeds to estimate aloaded plasma flux above the feature in operation 1530, and in aparallel operation 1535, to estimate the visibility of the feature attime t during the etch. The latter may be done as just described(assuming vertical sidewalls matching the feature's design layout), or amore nuanced initial guess may be employed (such as assuming somedefault approximate taper from feature opening to base, using a shapefound in a prior calculation, etc.). In any event, the shape is used toestimate a visibility which is then used in operation 1550, along withthe loaded flux from operation 1535, to index into the ROM look-up tableand determine an estimated EPE. The estimated EPE, however, isindicative of the shape of the feature. Accordingly, in FIG. 18, method1503 proceeds to operation 1572 where a decision is made as to whetherto update/refine the estimate of the feature's visibility (at time tduring the etch). If so, the method loops back to operation 1535,re-estimates the visibility based on the current estimated EPE, and thenproceeds again to operation 1550 where a more refined estimate of EPE isobtained by looking up the new re-estimated visibility in the ROMlook-up table. The iteration (of re-estimating visibility, and from it,re-estimating EPE) may continue a fixed number of times, or untilconvergence is reached with respect to visibility and/or EPE, asdictated by the decisional logic in operation 1572, after which, inoperation 1590, the initial design layout is modified based on there-estimated EPE (analogously to methods 1501 and 1502 of the priorfigures).

Of course, while loaded fluxes and visibility constitute an excellentcompact physical model (CPM) for assessing in-feature plasma flux(IFPF), other quantities characteristic of IFPF may be good proxies aswell, such as the direct physical characteristics of the in-featureplasma itself. For instance, it would be possible to implement a LUTdirectly in terms of actual ion and neutral plasma flux densities withinthe feature. See the discussion of FIG. 13B above.

As stated, the ROM look-up table (LUT) constitutes a very fast mechanismfor computing edge placement error (EPE) from the foregoing quantitieswhich characterize IFPF. However, in some cases, the ROM LUT may stillbe quite large, and hence various optimization procedures may beemployed to improve its performance. For instance, the LUT may be storedsorted based on one or more fields of the entries. Which field is usedas the primary sorting criteria, secondary sorting criteria, and soforth, may depend on the particular embodiment. In some embodiments, asmentioned above, the edge shape indicator field may be used as theprimary sorting criteria. Having the ROM table sorted in a meaningfulway increases the speed at which it may be searched to find the relevantentry or entries (by reducing the number of comparison operationsrequired between the value of the quantity being searched for—e.g., edgeshape indicator, plasma ion flux, plasma neutral flux, etc.—and thevalues held in the relevant fields of the table). In some cases, a LUTis pruned to remove entries that are redundant and/or unlikely to beneeded because they represent a region of etch space unlikely to beencountered in a particular application.

Oftentimes, the exact values of the relevant quantities which aresearched for are not present in the ROM LUT. When this is the case, onemay identify nearest-neighbor entries (those closest to the exactsearched-for values) and/or those which fit some criteria for being in aneighborhood around the exact sought value, and interpolate betweenthese entries. In some embodiments, for example, a multivariatepolynomial-based interpolation scheme may be employed.

In some embodiments, however, more sophisticated “interpolation” may beachieved with multivariate machine learning models. Depending on theembodiment, such machine learning models (MLM) may be unsupervised orpartially supervised, and such approaches may include those known in themachine learning and/or statistical science arts such as “GradientBoosting Machine,” “Deep Learning,” and “Distributed Random Forest.”

Regarding the “Random Forest” technique, see, for example: Breiman, Leo,“Random forests,”Machine learning 45.1 (2001): 5-32; Verikas, Antanas,Adas Gelzinis, and Marij a Bacauskiene, “Mining data with randomforests: A survey and results of new tests,” Pattern Recognition 44.2(2011): 330-349; and Segal, Mark R., “Machine learning benchmarks andrandom forest regression,” Center for Bioinformatics & MolecularBiostatistics (2004); each of which is hereby incorporated by referencein its entirety for all purposes.

Likewise, regarding the techniques generally referred to in these artsas “Gradient Boosting Machines,” see, for example: Friedman, Jerome H.,“Greedy function approximation: a gradient boosting machine,” Annals ofstatistics (2001): 1189-1232; Friedman, Jerome H., “Stochastic gradientboosting,” Computational Statistics & Data Analysis 38.4 (2002):367-378; and Schapire, Robert E., “The boosting approach to machinelearning: An overview,” Nonlinear estimation and classification,Springer New York, 2003, 149-171; each of which is hereby incorporatedby reference in its entirety for all purposes.

Finally, regarding the techniques generally referred to in these arts as“Deep Learning,” see, for example: Krizhevsky, Alex, Ilya Sutskever, andGeoffrey E. Hinton, “Imagenet classification with deep convolutionalneural networks,” Advances in neural information processing systems,2012; LeCun, Yann, et al. “Backpropagation applied to handwritten zipcode recognition,” Neural computation 1.4 (1989): 541-551; andSchmidhuber, Jurgen, “Deep learning in neural networks: An overview,”Neural Networks 61 (2015): 85-117; each of which is hereby incorporatedby reference in its entirety for all purposes.

These techniques can be used (again, depending on the embodiment) todetermine a sufficiently statistically accurate correlative relationshipbetween EPE and the quantities which would be used as described above toindex into the LUT (such as the plasma ion and neutral fluxes).

In general, a data-set similar to that used for constructing the ROM LUTwould also be used as a training set to develop (i.e., teach) the chosenmachine learning model (MLM). However, in training the MLM, it isfeasible to use a much larger version of this dataset than what would beefficiently searchable in the ROM LUT. I.e., the machine learning modelis trained offline with the full dataset to create anefficient-to-evaluate multivariate model of it, whereas it may not beefficient to search the full (training) dataset every time a newfeature's EPE was desired in the PPC procedure. Of course, once the MLMis trained based on a dataset—a portion of which could be selected toconstruct an efficiently searchable LUT—the MLM embodies a relationshipbetween EPE and plasma ion and/or neutral fluxes (for example) as does aplain LUT, and thus, on some level, the MLM does still make comparisonsbetween one or more quantities indicative of IFPF and a quantitycharacteristic of EPE in the evaluation of it's multivariate model,though the exact quantities and comparisons made would occur in thecontext of operation of the MLM as trained on the original dataset. Inany event, once the MLM is trained and validated against the originaldataset, it establishes a predictive mathematical relationship which maybe used to efficiently in a PPC procedure.

Yet another way of improving the accuracy of these PPC techniques is toemploy an etch time-based (or etch depth-based) iteration scheme. FIGS.19A and 19B provide a useful contrasting illustration. FIG. 19Aschematically illustrates the “one-time-step” approach and shows thatone goes from the top to the base of the feature in a single time stepto estimate EPE. Thus, the estimating of the various quantitiescharacteristic of IFPF is done just at the single etch time t (or singleetch depth), as well as the looking up of these quantities in the ROMlook-up table to arrive at the estimated EPE. This was illustrated, forexample, by the set of operations in FIGS. 15, 16, and 18. However, a“multi-time-step” approach may also be employed for calculating EPE.This is illustrated in FIG. 19B which shows multiple values of Δx_(EPE)calculated at multiple etch times (t₁, t₂, . . . t_(N)) which correspondto multiple etch depths (z₁, z₂, . . . z_(N)) down to the base of thefeature where finally a “final” value of Δx_(EPE) is calculated.

In the simplest multi-step version, there would be just two time steps.Thus, one would perform the estimation of quantities characteristic ofIFPF (e.g., loaded fluxes and visibility) at a first etch time t=t₁, usethese to estimate an EPE at time t₁ by comparing them to values in theROM look-up table corresponding to time t₁, and then repeat theprocedure for a second etch time t=t₂. However, the second time around,one may take advantage of the information gained during the firstiteration, and so forth in subsequent iterations. Thus, for example,because the feature has changed at time t₂ versus what it was at timet₁, the loaded fluxes and visibility kernel may be adjusted accordinglybased on this information, and these updated values then used to comparewith entries in the ROM look-up table which correspond to time t₂.

One may proceed analogously to break the calculation up into as manytime steps as desired. Such a multi-time-step methodology is illustratedin FIG. 20. Method 1504 in FIG. 20 proceeds analogously to methods 1501and 1502 shown in FIGS. 16 and 18 except that operations 1540 and 1550are performed first at a considered etch time of t_(i)=t₁ to estimate afirst EPE (in operation 1550). Method 1504 then proceeds to operation1573, where it is determined whether the current etch time t_(i) is lessthan the final total etch time. If it is, then the method increments thetime index “i” (t_(i+1)>t_(i)), and loops back to operation 1540 wherequantities characteristic of the IFPF are re-estimated, and thenproceeds to operation 1550 again to re-estimate EPE at the updated time.The iteration continues until in operation 1573 it is determined thatthe current time t_(i) is equal to or greater than the final/total etchtime, whereby the method proceeds to operation 1590 where the initialdesign layout is modified based on the final estimated EPE and/or theintermediate EPE calculated at the intermediate times, whereby themethod concludes. Additionally, one notes that it is possible to combinethe iteration scheme shown in FIG. 18—for arriving at better and bettervisibility estimates—with the iteration scheme in FIG. 20—which involvesiterative time/depth-slicing as just described.

Some masked etch processes may involve the etching of a multilayer stackof material where the different layers in the stack may have differentmaterial compositions. Assuming this is done with one mask (i.e., themultilayer etch processes is done subject to the same pattern ofphotoresist, then to do an effective PPC of a design layout, one isreally interested in the cumulative EPE corresponding to the entiremultilayer etch process (subject to the single photoresist pattern)rather than just the EPE associated with the etching of an individuallayer.

The procedures described above for calculating EPE through the use of aCPM-produced in-feature etch conditions for indexing into a ROM LUT maybe used to accomplish this, however in practice, there are severalvariations as to how this may be done. One way is to just build a largeROM LUT which corresponds to the entire multilayer etch process. Becausethe ROM LUT described above may include a time/depth field (see, e.g.,FIGS. 13B and 13C), this field provides a way to index into the LUT tolocate the appropriate EPE, which would then be a cumulative EPE for theentire process. In other words, building the ROM this way would already,in principle, effectively account for the presence of the differentmaterial layers, their thicknesses, etc. However, it is noted that forthis to be accurate in practice, it may be important to implement theiterative time/depth-slicing scheme just described with respect to FIG.20. For instance, in the context of a multilayer stack where differentlayers have different material compositions and, moreover, wheredifferent etch chemistries may be used to etch through the variouslayers, the accuracy of the estimated EPE may be dramatically improvedby matching the time/depth-slicing iterations to the depths (oretch-times) of the different layers. At these points, because thechemistries change, the EPE at the bottom of a single layer may only bewell-correlated with the characteristics of IFPF at the top of that samelayer, rather than at the top of the entire multilayer stack.

While using a single monolithic LUT representative of the entiremultilayer etch process (in a cumulative fashion) may be effective inmany circumstances, a potentially more flexible way of dealing with themultilayer stack issue is to build a set of smaller ROM LUT each ofwhich corresponds to one of the different layers of material in themultilayer stack. Flexibility is one advantage of such an approach inthat the same set of ROM LUT may be used for many different materialstack configurations, so long as there is a LUT corresponding to thematerial composition of each layer and it has entries going down tosufficient etch time/depth to account for the thickness of the layer ina particular stack configuration. Taking the simpler case of 2 layers ofdifferent materials—and thus 2 corresponding ROM LUT—one would firstindex into the LUT corresponding to the top layer to calculate the EPEassociated with an etch of this layer down to its base—i.e., just to thetop of the layer beneath—and then, second, with this first EPE in hand,use it to compute the visibility of the underlying second layer forpurposes of indexing into the second LUT to calculate a EPE at the baseof the bottom layer. This latter EPE then represents a cumulative EPEfor the 2-layer etch process. This is thus like a 2-step version of theiterative time/depth-slicing approach just described, but more flexiblein that each step uses a separate LUT. More than 2 layers could behandled analogously with additional layer/material-specific ROM LUT,using the previously computed EPE to index into the ROM LUT for the nextlayer down, and so forth. With either the single or multiple ROM LUTapproach for dealing with a multilayer stack, generally speaking, any ofthe procedures described above for calculating EPE through the use of aCPM and a ROM look-up table may be used, as would be appreciated by onehaving skill in the art.

However, with respect to the foregoing described treatment of multilayeretch processes using the multiple LUT (one per layer) approach, it isnoted that in certain circumstances complications may arise depending onthe composition of the layers and the details of the etch process(es)involved. In some embodiments, these complications may in general arisewhen the etching of an underlying layer (second layer, third layer,etc.) depends on some characteristic or result of the etching of one ormore layers above it which are not accounted for in the layer-specificLUT corresponding to the underlying layer. For instance, the verypresence of the layers above the layer being etched (i.e., the layerswhich have already been etched though) may change and/or affect thechemistry of the process which etches the underlying layer. If thisaltered chemistry was not accounted for by the EPM which was used tobuild the layer-specific LUT, then use of said LUT will not yieldaccurate estimates of the cumulative EPE. In such cases, the remedy maybe building the LUT specific to the underlying layer using an EPE whichdoes take the presence of the layers above it into account. That beingsaid, it should also be noted that the mere shadowing effects of thelayers above the layer being etched may actually be well-accounted forby the layer-specific LUT through the visibility kernel. However, forthe shadowing effects of the overlying layer(s) to be well-accountedfor, any changes in their shapes during the etch process operating onthe underlying layer should also likely be considered. Again, one ofskill in the art should also appreciate that the layer-by-layer approachjust described is a time-slicing approach similar to what is describedabove with respect to FIG. 20—t_(i) corresponding to the etching throughof the first layer in the stack, t₂ corresponding to etching through thesecond layer in the stack, and so forth.

Finally, it is noted that the foregoing techniques for generatingproximity-corrected design layouts for photoresist for use in photomaskgeneration and semiconductor etch operations may be implemented in acomputer system. Such a computer system would typically have one or moreprocessors, and one or more memory units, the latter of which wouldtypically store computer-readable instructions (for execution on the oneor more processors), the instructions implementing any of the foregoingmethodologies. In some embodiments, such systems may operate by readingan initial design layout from a computer-readable medium, and writingthe final proximity-corrected design layout to a computer-readablemedium. The techniques and operations disclosed herein may also beembodied in computer-readable instructions stored on one or morecomputer-readable media.

Likewise, plasma etch systems for etching semiconductor substrates mayinclude a computer system as just described, as well as aphotolithography module configured to (i) receive a proximity-correcteddesign layout for photoresist from the computer system, (ii) form a maskfrom the proximity-corrected design layout, and, optionally at a latertime, (iii) perform a photolithography operation using the mask totransfer a layer of photoresist to a semiconductor substratesubstantially conforming to the proximity-corrected photoresist designlayout. Such plasma etch systems would then also include a plasma-etchercomponent (e.g., with a reaction chamber, plasma generation hardware,wafer support, etc.) which is configured to generate a plasma which thencontacts the semiconductor substrate and etches those portions of thesubstrate surface not covered with the photoresist transferred by thephotolithography module. Operation (iii) may be performed repeatedly fora given mask produced in (ii).

By applying the foregoing described principles, techniques, andmethodologies, a physics-aware pattern proximity correction (PPC)solution may be provided to IC device designers. For given processingrecipe and material stack, EDA (electronic design automation) tools maybe implemented with the capability of predicting (approximately, butwith good accuracy) the etch transfer function for a given incomingdesign layout for photoresist—as explained with respect to FIG. 12, thishas the capability of significantly lowering photomask development costsand dramatically shorten time to solution. It is further envisioned thatthrough the foregoing described principles, techniques, andmethodologies, that process window libraries may be made available fromwhich sensitivity matrices can be generated rapidly with minimalconsumption of test wafers and time-intensive physical experimentation.These may be bundled with system sales or sold separately, possibly withperiodic updates for new films stacks and processes. In addition, insome embodiments, it may be possible to create designs that were made tofit a specified process rather than the process necessarily beingdeveloped to fit a given design. This potentially would allow toolselections to be made at time of design (locked-in (or locked-out)early), and thereby a level of minimum variability could be designed-inat the outset. Moreover, the ability to predict edge placement errorfrom computational principles early on may allow for earlyfault-detection and classification, not otherwise easily possible.

LUT Down-Selecting—Etch-Sensitive Parameter Space Explorer (EPSE)

Strategies for generating a LUT or related model for predicting andultimately correcting a design layout to account for particular etchprocesses might naturally employ a wide range of possible design layoutstructures (1D & 2D shapes, widths, pitches, etc.) and produce LUTentries covering a very wide range of such structures. In other words,such LUT will have a very large number of entries (data points), perhapsmillions. Using such a large LUT requires a large sampling, but maycontain many redundant structures that are unneeded for covering usefuletch space behavior of the process layer being targeted. Finding anappropriate coverage for the LUT is sometimes referred to asetch-sensitive parameter space exploration, or EPSE. A limited analogycan be made with existing tools for sampling the imaging space forfinding the appropriate coverage to capture the process behavior afterlithography. The following references are incorporated herein byreference in their entireties:

-   Tawfic et al., Feedback Flow to improve Model Based OPC Calibration    Test Pattern, Proc. SPIE, Vol. 6521, 65211J (2007)-   Oberschmidt et al., Automation of Sample Plan Creation for Process    Model Calibration, Proc. SPIE, Vol. 7640, 76401G (2010)-   Abdo et al., The feasibility of using image parameters for test    pattern, Proc. SPIE, Vol. 7640, 76401E (2010)-   Sun et al., Optimizing OPC data sampling based on “orthogonal vector    space, Proc. SPIE, Vol. 7973, 79732K (2011)-   Lorusso et al., Model calibration and validation for pre-production    EUVL, Vol. 8322, 83221L (2012)

Without an appropriate reduction of entries, it can be difficult,time-consuming, and inefficient to both generate and use such a broadLUT. Generating a LUT with many entries may create difficulties by:

-   -   Requiring extensive metrology runtime to experimentally measure        the structures to be used for the LUT (e.g. CD-SEM, Critical        Dimension-Scanning Electron Microscopy measurements), often at        several steps in the process    -   Potentially adding metrology errors by measuring many structures    -   Repeating running of the EPM to generate enough points to        populate the LUT

Using a large LUT to generate a predicted the edge placement error of aninput layer may create difficulties by:

-   -   Requiring long computational runtime to predict the edge        placement error of the input layer or the specific process        related etch conditions    -   Adding more noise in generating the predicted edge placement        error due to the potential errors in some of the LUT entries        (i.e., the prediction is less accurate and/or less robust)

In certain embodiments, a full data set, which may represent a largenumber of data points such as entries or potential entries in a LUT asdescribed herein, is “pruned” or made sparser by selectively eliminatinga large fraction of the data points, many of which may be considered asredundant. The pruning may be performed to produce a streamlined LUT fora specific type of mask or structure set (e.g., covering a featuregeometrical space appropriate for a particular type of memory or logicIC design).

An aspect of this process is illustrated graphically in a simpletwo-dimensional plot (FIG. 21) containing a full data set (shown asblack points) in etch parameter space and a subset (shown as white/graypoints) used for a final design layout LUT. As an example, parameterssuch as EPE, IFPF quantities (e.g., ion flux, radical flux, and/orneutral flux), etc. are provided on axes of the multi-dimensional etchparameter space (only two dimensions are shown in the figure, but moredimensions can be thought of). For purposes of developing a compact LUT,these may be parameters that are used to index into the LUT. In thefigure, the white/gray dots provide a distribution of points that aredistributed throughout the entire range of parameter space in whichdesign geometry and etch conditions are likely to reside. Additionally,the selected points are distributed relatively evenly over the range.

Stated another way, methods may down-select from a list of “P”structures (LUT entries or data points in etch parameter space) to amuch smaller list of N<<P structures. The N selected structures (datapoints) are representative of an etch process and/or design type (withassociated specific structures). The N structures are selected tocapture an appropriate range and density of etch effects that areexisting for the particular process/structures that the LUT willcharacterize. Therefore, the etch model (LUT) will rely only upon thoserepresentative structures (LUT entries), and not others or unnecessaryones.

For purposes of down-selecting LUT entries, the term “etch space”generally refers to a multi-dimensional space defined by layoutstructure geometry, EPE, and derived parameters from characterizing infeature etch condition (e.g., IFPF characteristics). An “edge” or a“point” along this edge in etch space may include information such as anEPE value (i.e., a result) and some relevant etch parameter values(e.g., IFPF related parameters). The points may serve as (or beassociated with) entries in a LUT. While much of this discussion ispresented in terms of selecting points for entries in a LUT, theconcepts apply with equal force to identifying appropriate edges or“points” for training a model such as a machine learning model that canpredict EPE as a function of structure geometry and/or in feature etchproperties.

As it can be appreciated, over the universe of commercially feasiblemask design layouts, there are very many data points for a given etchprocess. As an example, a mask typically contains billions of structuresat the resolution of a lithography process. Each such structure (whichmay be described as a polygon) has dedicated optical and etchproperties, locally and globally with respect to its locations withinthe mask. Each structure and its associated properties may be viewed asa series of data points. Ideally a small LUT using only a relatively fewof the billions of structures will preserve the usefulness of a muchlarger LUT using all structures. As an example, a final LUT for aparticular mask associated with a dedicated fabrication process mayemploy fewer than about 1000 entries (each associated with a differentfeature structure), or fewer than about 500 such entries, or fewer thanabout 200 such entries.

A process of generating a LUT or other model for predicting andcorrecting for a design layout to account for a dedicated etch processcondition as described above is illustrated in FIG. 22. As shown, a LUTgenerating process 2201 begins by receiving layout geometry and otherrelevant inputs for modeling a wide range of etch conditions. See block2203. Such inputs may include numerous test structures (mask or layoutgeometries), resist profiles, etch reactor parameters such as plasmaconditions, etc. expected to be encountered in practice. To this end,the process may employ a test mask having features spanning the entirerange of structures expected to be encountered for several potentialtechnology nodes in logic and memory. A full range of expected features1D & 2D shapes, sizes, pitches, etc. may be employed, for whichsimulated resist profiles for each of those structures are required.Additionally, a range of reactor conditions potentially encounteredduring commercial fabrication are identified as inputs. Loadings andvisibility kernels may be considered at this stage. Some ElectronicDesign Automation tools employ empirical compact modeling tools (relyingsolely on experimental data) to account for loadings and visibilitykernels.

Typically, a test mask is not representative of a real logic mask.Rather, a test mask contains a wide range of structures (1D L/S, 2 Bars,3 Bars, 2D end-of-line tip-to-tip, tip-to-line, and complex 2Dstructures) which may be provided with various pitch/CD combinations. Insome cases, the combinations are using a technique such as Design ofExperiment (DOE). Such variations may cover multiple technology nodes. Areal logic mask is constructed according to the chip functionalitiesthat need to be transferred according to process assumptions, obeying tospecific geometrical constraints. In lithography, a test mask is usedfor calibrating an optical and resist model. The calibrated model isapplied to the real logic mask for proximity corrections (OPC) toimprove its printability performance.

Operation 2203 involves generating a first pass LUT that is general forvarious masks that an electronic design manufacturer might employ with agiven etch process. E.g., it may employ a test mask. As such, operation2203 anticipates the range of geometries and generates a very largerange of features for generating the first pass LUT (beforedown-selection). Ultimately, the resulting library can be re-used forother processes covering the same or similar process conditions and maskgeometries.

The wide range of feature geometries for generating the first pass orgeneral LUT may be given by the lithography step, which is the step oftransferring a pattern from a resist layer to an etch layer.Transferring a geometry from a mask to a pattern in resist requiresimaging optimization for the printability performance. This imagingoptimization may include mapping the imaging space and selectingstructures of interest for calibrating and verifying optical models.These structures may be employed to generate the first pass LUT.

Using all these various features (geometries) and lithography processinputs, the etch process, and particularly the EPE, is modeledrepeatedly for numerous data points, potentially millions or evenbillions. As explained such modeling may be conducted with an EPM,although this aspect of the disclosure is not so limited. Alternatively,some or all of etch profiles (and associated EPEs) may be measured afterphysically conducting the process for a variety of features. Regardless,a full set of data points (feature geometries, IFPF and/or otherfeature-relevant etch conditions, and EPE values) in etch parameterspace is generated. See block 2205. All these data points could be usedas entries in a LUT for design layout prediction and ultimatelycorrection, but as explained such a LUT would not be efficient to use.Such LUT may be viewed as including entries corresponding to all theblack data points in FIG. 21.

A goal at this stage is to down-select to a set of N data points toproduce a more efficient to use LUT, e.g. one containing only entriescorresponding to the white/gray data points in FIG. 21 and suitable foruse with a particular design layout or group of related design layouts.This may be accomplished through any of a number of down-selectionprocesses, some of which are described below. Selection or receipt ofthe down-selection process or code/instructions for implementing thealgorithm is depicted in block 2207. Thereafter, the down-selectionprocess is executed to select only the data points to be used as entriesin the smaller LUT suitable for use with a particular design or designclass. See block 2209. Note that in some implementations, thedown-selection process includes a manual component; e.g., a trainedapplication engineer views a relevant depiction of etch process space toensure that the selected data points adequately cover the full range ofexpected process/feature space. More typically, the process is fullyautomated (e.g., following a methodology/algorithm defined with userspecifications).

A more detailed example is provided in FIGS. 23A-E. Note that there areat least two levels of design layout correction coming in this context:lithography and etch. Additionally, only one physical layer level istypically considered for the etch process, although multi-layer stacksmay be considered (as existing in multiple patterning solutions forimmersion lithography).

As shown in FIG. 23A, an iterative process 2301 is employed to generatea layout design-specific streamlined LUT as described herein. Theprocess begins with generation of, or receipt of, a test mask or clippedtest mask (i.e., one that contains only the polygons of interest) thatmay be provided in a GDS format (e.g., a GDSII format). See block 2303.GDS is an example of a standard format for design layouts that containthe so-called polygons: there are a few including GDSII “GraphicDatabase System” and OASIS (Open Artwork Interchange Standard). Afterreceiving the test mask (or clipped test mask), a gauge file readerreads the test mask, as is conventional in some optical proximitycorrection contexts, to view locations of the features of interest to bemodeled. See block 2305. Gauge files may include coordinates in X/Y,labelling conventions, CD/pitch design as drawn in the layout, measuredCD after lithography step, etc.

A gauge file reader provides a rigorous description of the locations ofvarious edges of structures on an overall design layout. It presentsthese locations in terms of distances between, e.g., horizontal edges,and/or dimensions and shapes of polygons. It is represented on a layoutas a one dimensional cutline that is added on top of the polygon forvisualization. The gauge file is prepared for a particular process step(e.g., after lithography or after an etch step). The gauge file depictslocations of features by providing pieces of information about the twofeature edges of particular interest on the pattern. In the integratedcircuit industry, gauges have been defined with respect to lithographyand in the domain of OPC, but in the context of this disclosure, it isalso used for characterizing an etch pattern

A test mask or clipped test mask containing one of the structures ofinterest is provided to a rigorous resist simulator (e.g., KLA-TencorProlith in this example) that predicts optical and resist effects inprinting a mask on a wafer. See block 2307. This producesthree-dimensional shapes that can be used to feed other etch predictioncomponents (e.g., updated compact physical models, reduced order models,surface kinetic models, and the like). The gauge file values are used asinputs to provide guidance on which edge or point along the edge is ofinterest for the lithography step, but in the context of this disclosurecan be also used for the etch step.

The output of the rigorous simulators (e.g. Prolith) nominallyrepresents the pattern that would be printed on a photoresist using thetest mask (e.g. 3D file format such as StereoLithography format, .stl),but not accounting for the subsequent etching process. In certainembodiments, the representation is converted to a file format that isconvenient for use with etch modeling routine as described herein. Seeblock 2309. An example of such file format is the CPI file format.

The appropriately formatted resist profile feature pattern is thenprovided to a compact physical model (CPM) as described herein. Seeblock 2311. The compact physical model converts the resist profile ofthe structure/feature information and appropriate process conditions tocharacteristics of in feature fluxes (e.g., IFPFs), which may be used toindex into a LUT as described elsewhere herein. See block 2313.

To reiterate, as illustrated in FIG. 23A, the process 2301 iterates overmany structures/features contained in the test mask. For each newstructure, a rigorous lithographic simulation routine (lithographymodeling) is performed on the structure as illustrated in blocks 2307and 2309. The resist profile feature is then evaluated using a CPM asillustrated 2311 to generate the appropriate in-feature fluxes or otherparameters that are used to index into the entries in the LUT asindicated at 2313. This may be a previously generated LUT that hasentries for generating EPEs for a large range of in feature fluxes.

When all relevant features or structures from the test mask areconsidered (e.g., applied to the CPM and the resulting fluxes applied toa large LUT), the relevant EPE values will have been determined. At thispoint, the data set for the design(s) under consideration can bevisualized. Collectively, the data points represent too many entries fora practical LUT. Thus, a down-selection process is performed to reducethe number of entries to only those needed to appropriately characterizethe etch space of the process in the realm of the design layout(s) underconsideration.

The down-selection process may be implemented via a technique depictedin process blocks 2315 and 2317. Operation 2315 characterizes thegenerated multidimensional etch values to identify regions or pointssuitable for inclusion in the smaller version of the LUT. Through theprocess illustrated in operation 2315, the methodology produces a reportof prioritized locations for the LUT as depicted at block 2317.

FIG. 23B illustrates a process by which the test mask provided in block2303 is evaluated and its structures organized for optical lithographyand other analysis. The operations depicted in FIG. 23B may beconsidered to represent those associated with block 2305 from FIG. 23A.As shown, a customer or other developer of a fabrication processprovides as inputs a test mask (or clipped test mask) in appropriateformat (e.g., a standard layout format such as GDSII or otherappropriate file format) and/or an appropriate gauge file as illustratedat 2321. Early in the process, a file reader may iterate through thetest mask and identify all structures of interest as illustrated in anoperation 2323. Further, during this stage, loadings may be consideredbased on the environment of individual structures to be modeled. Incertain embodiments, loadings are calculated using an appropriate EDAtool (e.g., Calibre from Mentor Graphics Corporation). Such tools cancalculate pattern density at different ranges, either local or global.In this context, the loading can be described as a value that can bede-convolved from short range to mid-range to long range distance wise.

This process produces a number of structures that are identified andgrouped, these structures being found in the test mask. The structuresmay have one-dimensional and two-dimensional geometries as illustratedin the patterns associated with an operation 2325. Also, as illustrated,loadings associated with the different structures may be calculated asillustrated at a block 2327, but such calculations may be unnecessary ifthey were previously calculated such as at operation 2323.

FIG. 23C illustrates operation 2307 from FIG. 23A. In the depictedembodiment, an individual test mask structure as produced in operation2325 and/or 2327 is provided along with optical scanner conditionsand/or information about the photoresist stack on which the test maskstructure will be printed. See operation 2329. Such information may beprovided to Prolith or other rigorous resist simulators. See operation2331. The output is a photoresist profile for each of the individualtest mask structures considered. See 2333.

FIG. 23D illustrates a process for generating in-feature etch fluxeswhich may be used in a LUT or other model for determining EPE. Theoperations and features illustrated in FIG. 23D may represent operations2309 and 2311 from FIG. 23A. As depicted in FIG. 23D, the resistprofiles may be converted to an appropriate file format recognized bythe compact physical model. See block 2335. Of course, this conversionoperation is optional and is not necessary if the compact physical modelcan work directly from the resist profiles. The compact physical modeloperates on the resist profiles along with, optionally, such otherinformation as needed to produce fluxes as locations of the structure ofinterest, loading factors for structure of interest, and reactor etchconditions such as ion energy angular distributions. See 2337.Collectively, these inputs (e.g., the resist profile along withlocations, loading factors, and ion energy angular distribution for thestructure of interest) are evaluated by a previously generated compactphysical model as illustrated at 2339. This operation outputs in-featurefluxes as illustrated at 2341.

As illustrated in FIG. 23E, the in feature fluxes produced to 2341 areapplied to a previously generated lookup table for the etch processunder consideration. See 2343. The produces a series of data pointsrepresenting edge placement error as a function of the fluxes input at2341. A multivariate model or other tool produces a representation ofthe data output is illustrated in block 2345. The edge placement errors,in-feature fluxes, loadings, etc. represented in the multidimensionalspace are considered for the etch space exploration as illustrated at2347. From this, the down-selection of data points and hence LUT entriesmay be performed for the layout design(s) under consideration.

Various techniques may be employed to remove data points (or select datapoints) for the compact design-specific LUT. Generally, the selectedpoints should produce a pruned LUT that accurately represents—nearly asaccurately as the unpruned LUT—EPEs for the structures encountered inthe layout patterns for the IC designs for which the LUT is used. Invarious embodiments, the data points and entries of a pruned LUT shouldspan nearly the full range of relevant structures in the unpruned LUT(i.e., the data space of the points/entries in the unpruned LUT). Notethat in some implementations the initial unpruned LUT does not containat least some useful information from the pruned one because the initialunpruned LUT was prepared in a potentially naïve manner. In variousembodiments, the data points and LUT entries should fully representregions of etch parameter space where in-feature fluxes and/or EPE varymost rapidly (sometimes referred to as “regions of high etchsensitivity”).

In some approaches, the down-selection process considers deviations inplasma flux within the multidimensional space, and separates the pointsfor the LUT according to a defined spacing criteria. For example, theprocess may create a grid based on a plasma flux parameter within themultidimensional space, and select the points for the compact LUT basedon defined separation distances within the grid. In some embodiments, agoal is to make the points for the LUT substantially equally spacedwithin the grid. Such approach may (or may not) additionally account forregions of high sensitivity within the data.

Some approaches look for sensitivity of one parameter (e.g., edgeplacement error) with respect to variations in a different parameter(e.g., plasma ion flux or visibility kernel). Such variations may beconsidered with respect to feature structure (directly or indirectly viain-feature information such as visibility kernels, etchant fluxes,etc.). In regions of high sensitivity, the down-selection method mayclosely space the data points (LUT entries) to capture with highresolution the variation of the sensitive parameter. In regions of lowersensitivity, a lower density of data points (LUT entries) is provided.This approach produces more entries in LUT in regions where the EPEchanges rapidly as a function of changes in, e.g., IFPF parameters. Insome implementations, the densities of LUT points in different regionsof parameter space are proportional to the sensitivities in thoseregions. In some embodiments, sensitivity can viewed as a partialderivative of edge placement error with respect to parameters thatinfluence EPE such as the various above-described quantitiescharacteristic of IFPF.

Thus, in certain embodiments, for each potential entry, thedown-selecting technique calculates a sensitivity metric for the entry.The sensitivity metric indicative of the magnitude of the partialderivative of the quantity characteristic of EPE with respect to aquantity characteristic of IFPF (d[EPE]/d[IFPF]) evaluated at a value ofthe quantity characteristic of IFPF (e.g., IFPIF, IFPNF, and/or IFPDF).The process then selects a subset of entries from the set of potentialentries such that, e.g., the average of the sensitivity metric over thesubset is higher than the average of the sensitivity metric over thefull set.

In some cases, the down selection or pruning reduces the size of a LUTby at least about 20% (in terms of number of entries) or by betweenabout 20% and 50%. In some cases, the subset of entries is selected suchthat of the 25% of the entries in the full set having the highestsensitivity metrics, at least 5% are included in the subset. In somecases, the subset of entries is selected such that of the 10% of theentries in the full set having the highest sensitivity metrics, at least2% are included in the subset. In some embodiments, the subset ofentries is selected such that when the subset is sorted based on thequantity characteristic of IFPF, the density of entries in the subset(relative to the quantity characteristic of IFPF) changes in proportionto the average sensitivity metric (calculated over the group of entrieswithin the subset used to estimate the density) over at least about 75%of the entries selected for the subset. In some implementations, the EPEpredictions from a LUT prepared by down selection has substantially thesame error rate and sometime an improved error rate (measured in e.g.,RMS) compared to EPE predictions from the initial unpruned LUT.

In some embodiments, the method involves detecting “high sensitivityregions” in a plurality of features to be etched into a material stack.A down-selection method may include the following operations: (a)choosing a plurality of potential high sensitivity regions in theplurality of features, each potential high sensitivity regioncorresponding to a particular edge of a feature; (b) for each potentialhigh sensitivity region, calculating a sensitivity metric correspondingto the particular edge associated with the potential high sensitivityregion, the sensitivity metric indicative of the magnitude of anestimated partial derivative of a quantity characteristic of an edgeplacement error (EPE) corresponding to the edge with respect to aquantity characteristic of an in-feature plasma flux (IFPF)corresponding to the feature, the partial derivative estimated withrespect to a value of said quantity characteristic of IFPF correspondingto the feature and chosen process conditions; and (c) identifying highsensitivity regions in the plurality of potential high sensitivityregions based on the sensitivity metric.

Various algorithmic and statistical mechanisms may be employed forfinding sensitivity in etch space. One approach employs principalcomponent analysis or other implementation of singular valuedecomposition (SVD). The process may be implemented to create a grid ofprincipal components. As a result, one has a reduced dimensionalityspace in which the axes represent vectors (principal components) overwhich most variation occurs in the multi-dimensional space of theparameters relevant to EPE. The data points selected for inclusion inthe LUT are spaced along the principal components so that most of thevariation in the data is represented and regions of high sensitivity arewell covered. The down selection process can also identify sensitivityusing principal component analysis, data analytics, machine learning(e.g., neural networks), etc.

A decision not to include an entry in the LUT associated with an edge ofthe second selected feature while including an entry associated with anedge for a first selected feature may be made based (at least in part)on the similarity of an etch flux characteristic (e.g., an ion fluxcharacteristic or a neutral flux characteristic) of the first and secondedges. For example, the decision to not include the second entry in theLUT may be made when the etch flux characteristic of the first andsecond IFC values is within 5%. Similar decisions can be made for edgesassociated with third and additional edges that provide etch fluxcharacteristics with a similar degree of similarity to the etch fluxcharacteristics of the first edge.

FIG. 24 illustrates in a general format how information for downselecting LUT entries may be collected. In this example, flux species(e.g., radical or other plasma flux species) may be calculated atvarious positions in one or more feature structures. FIG. 24 depicts onesuch feature. The flux information may be generated with a compactphysical model as described herein or with another tool. The flux valuesat various locations within the feature structure are then used toidentify multiple parameters associated with lookup table entries.Examples of such features include maximum and minimum values of a fluxspecies in the feature, a slope of the flux magnitude from position toposition within the feature, the curvature of the flux profile atlocations within the feature, etc. Other information associated with thefeature or particular positions in the feature may be collected. Edgeplacement errors for points in the feature structure are an example ofsuch information (when completing the transfer from the lithography stepto the layer of interest after etch within the process stack).

As shown in FIG. 24, a cross-section of a resist profile and associatedpositions of interest, depicted as stars, where fluxes are calculatedsuch as with a CPM. In the figure, there are four such positions shownon the left side of the feature and four on the right side, with oneadditional position in the middle, i.e., the center of the base of thefeature. Other numbers of positions may be employed; for example, atleast about five positions on each of the left and right sides, alongwith one additional position in the middle. In many cases, the method isdesigned so that there are about eight to fifteen positions in the leftside, and about eight to fifteen positions on the right side, with oneadditional position in the middle. Regardless of how many such positionsare selected, each one identifies a point where a flux or other directparameter is calculated.

Various derived parameters may be calculated from the direct parameter.For example, if the direct parameter is a measure of radical flux,derived parameters associated with that radical flux distribution may bethe local slope of the radical flux, a curvature of the radical flux,ratios of the radical flux with at various adjacent positions in thefeature, and other physical and geometric parameters associated with oneor more flux values in the etched feature. In some embodiments,additional parameters associated with a feature position, such as theedge placement error at the position, may be associated with the otherparameters. Still further, parameters associated with the entire featuresuch as a maximum and minimum values of the flux distribution may beemployed.

Collectively, the information used for down selecting characterizes theentire feature etch space, a subset of points within the feature, orindividual points within the feature. Any one or more of these pieces ofinformation may be associated with one or more LUT entries.

In some cases the information about individual points or collections ofpoints within a feature is collectively provided as a data set which canbe used to visualize the distribution of potentially relevant pointswithin an etch parameter space. These parameters may also provide a goodindication of the sensitivity of particular etch parameters with respectto one another or of the edge placement error with respect to particularetch parameters. For example, an EPE or flux slope or curvature in thevicinity of a feature point may indicate the sensitivity to etchparameters.

In various embodiments, the data set is provided in a multidimensionaletch parameter space, where the individual dimensions of the spacerepresent the various parameters used to characterize the points orfeatures presented in the data set. With this data set distributed inthe multidimensional space, principal component analysis or a relatedtechnique for identifying variations in the data set is conducted. Theprincipal components or other indicators of variability or sensitivityin the data set helps select points for inclusion in a down selectedlookup table. For example, points that are distributed across the fulllength of one of the more important principal components (e.g., thefirst, second, and/or third principal components) are useful foridentifying points to include in a down selected lookup table.

In some implementations, the use of a smaller LUT (one with relativelyfew entries) provides one or more of the following advantages:

-   -   Reduction of the number of time-consuming EPM runs or physical        measurements by automatic structure selection method    -   Reduction of the computational time to make predictions and        ultimately corrections to a design layout, by limiting the        number of structures in the LUT    -   Increase the accuracy of an etch-based layout design simulator        by selecting the structures based on a defined set of parameters    -   Focus on structures that are sensitive to etch conditions (e.g.,        IFPF)        System Controllers

A system controller may be used to control etching operations (or otherprocessing operations) in any of the above described processingapparatuses, such as the CCP etcher apparatuses shown in FIGS. 9A-9C,and/or the ICP etcher apparatus shown in FIG. 10. In particular, thesystem controller may implement an optimized EPM as described above andadjust operation of an etcher apparatus in response to computed etchprofiles generated using the optimized EPM (as described above).

An example of a system controller in communication with an etcherapparatus is schematically illustrated in FIG. 10. As shown in FIG. 10,system controller 1050 includes one or more memory devices 1056, one ormore mass storage devices 1054, and one or more processors 1052.Processor 1052 may include one or more CPUs, ASICs, general-purposecomputer(s) and/or specific purpose computer(s), one or more analogand/or digital input/output connection(s), one or more stepper motorcontroller board(s), etc.

In some embodiments, a system controller (e.g., 1050 in FIG. 10)controls some or all of the operations of a process tool (e.g., etcherapparatus 1000 in FIG. 10) including the operations of its individualprocess stations. Machine-readable system control instructions 1058 maybe provided for implementing/performing the film deposition and/or etchprocesses described herein. The instructions may be provided onmachine-readable, non-transitory media which may be coupled to and/orread by the system controller. The instructions may be executed onprocessor 1052—the system control instructions, in some embodiments,loaded into memory device 1056 from mass storage device 1054. Systemcontrol instructions may include instructions for controlling thetiming, mixture of gaseous and liquid reactants, chamber and/or stationpressures, chamber and/or station temperatures, wafer temperatures,target power levels, RF power levels (e.g., DC power levels, RF biaspower levels), RF exposure times, substrate pedestal, chuck, and/orsusceptor positions, and other parameters of a particular processperformed by a process tool.

Semiconductor substrate processing operations may employ various typesof processes including, but not limited to, processes related to theetching of film on substrates (such as by atomic layer etch (ALE)operations involving plasma-activation of surface adsorbed etchants,see, e.g., U.S. patent application Ser. No. 14/539,121, filed Nov. 12,2014, and titled “ADJUSTMENT OF VUV EMISSION OF A PLASMA VIA COLLISIONALRESONANT ENERGY TRANSFER TO AN ENERGY ABSORBER GAS,” which is herebyincorporated by reference in its entirety for all purposes), depositionprocesses (such as atomic layer deposition (ALD), by plasma-activationof surface adsorbed film precursors), as well as other types ofsubstrate processing operations.

Thus, for example, with respect to a processing apparatus for performingplasma-based etch processes, the machine-readable instructions executedby a system controller may include instructions for generating acomputed etch profile from an optimized EPM and adjusting operation ofthe plasma generator in response to the computed etch profile.

System control instructions 1058 may be configured in any suitable way.For example, various process tool component subroutines or controlobjects may be written to control operation of the process toolcomponents necessary to carry out various process tool processes. Systemcontrol instructions may be coded in any suitable computer readableprogramming language. In some embodiments, system control instructionsare implemented in software, in other embodiments, the instructions maybe implemented in hardware—for example, hard-coded as logic in an ASIC(application specific integrated circuit), or, in other embodiments,implemented as a combination of software and hardware.

In some embodiments, system control software 1058 may includeinput/output control (IOC) sequencing instructions for controlling thevarious parameters described above. For example, each phase of adeposition and/or etch process or processes may include one or moreinstructions for execution by the system controller. The instructionsfor setting process conditions for a film deposition and/or etch processphase, for example, may be included in a corresponding deposition and/oretch recipe phase. In some embodiments, the recipe phases may besequentially arranged, so that all instructions for a process phase areexecuted concurrently with that process phase.

Other computer-readable instructions and/or programs stored on massstorage device 1054 and/or memory device 1056 associated with systemcontroller 1050 may be employed in some embodiments. Examples ofprograms or sections of programs include a substrate positioningprogram, a process gas control program, a pressure control program, aheater control program, and a plasma control program.

A substrate positioning program may include instructions for processtool components that are used to load the substrate onto pedestal and tocontrol the spacing between the substrate and other parts of processtool. The positioning program may include instructions for appropriatelymoving substrates in and out of the reaction chamber as necessary todeposit and/or etch film on the substrates.

A process gas control program may include instructions for controllinggas composition and flow rates and optionally for flowing gas into thevolumes surrounding one or more process stations prior to depositionand/or etch in order to stabilize the pressure in these volumes. In someembodiments, the process gas control program may include instructionsfor introducing certain gases into the volume(s) surrounding the one ormore process stations within a processing chamber during film depositionand/or etching operations on substrates. The process gas control programmay also include instructions to deliver these gases at the same rates,for the same durations, or at different rates and/or for differentdurations depending on the composition of the film being depositedand/or the nature of the etching process involved. The process gascontrol program may also include instructions for atomizing/vaporizing aliquid reactant in the presence of helium or some other carrier gas in aheated injection module.

A pressure control program may include instructions for controlling thepressure in the process station by regulating, for example, a throttlevalve in the exhaust system of the process station, a gas flow into theprocess station, etc. The pressure control program may includeinstructions for maintaining the same or different pressures duringdeposition of the various film types on the substrates and/or etching ofthe substrates.

A heater control program may include instructions for controlling thecurrent to a heating unit that is used to heat the substrates.Alternatively or in addition, the heater control program may controldelivery of a heat transfer gas (such as helium) to the substrate. Theheater control program may include instructions for maintaining the sameor different temperatures in the reaction chamber and/or volumessurrounding the process stations during deposition of the various filmtypes on the substrates and/or etching of the substrates.

A plasma control program may include instructions for setting RF powerlevels, frequencies, and exposure times in one or more process stationsin accordance with the embodiments herein. In some embodiments, theplasma control program may include instructions for using the same ordifferent RF power levels and/or frequencies and/or exposure timesduring film deposition on and/or etching of the substrates.

In some embodiments, there may be a user interface associated with thesystem controller. The user interface may include a display screen,graphical software displays of the apparatus and/or process conditions,and user input devices such as pointing devices, keyboards, touchscreens, microphones, etc.

In some embodiments, parameters adjusted by system controller may relateto process conditions. Non-limiting examples include process gascompositions and flow rates, temperatures (e.g., substrate holder andshowerhead temperatures), pressures, plasma conditions (such as RF biaspower levels and exposure times), etc. These parameters may be providedto the user in the form of a recipe, which may be entered utilizing theuser interface.

Signals for monitoring the processes may be provided by analog and/ordigital input connections of the system controller from various processtool sensors. The signals for controlling the processes may be output onthe analog and/or digital output connections of the process tool.

Non-limiting examples of process tool sensors that may be monitoredinclude mass flow controllers (MFCs), pressure sensors (such asmanometers), temperature sensors such as thermocouples, etc.Appropriately programmed feedback and control algorithms may be usedwith data from these sensors to maintain process conditions.

The various apparatuses and methods described above may be used inconjunction with lithographic patterning tools and/or processes, forexample, for the fabrication or manufacture of semiconductor devices,displays, LEDs, photovoltaic panels and the like. Typically, though notnecessarily, such tools will be used or processes conducted togetherand/or contemporaneously in a common fabrication facility.

In some implementations, a controller is part of a system, which may bepart of the above-described examples. Such systems can comprisesemiconductor processing equipment, including a processing tool ortools, chamber or chambers, a platform or platforms for processing,and/or specific processing components (a wafer pedestal, a gas flowsystem, etc.). These systems may be integrated with electronics forcontrolling their operation before, during, and after processing of asemiconductor wafer or substrate. The electronics may be referred to asthe “controller,” which may control various components or subparts ofthe system or systems. The controller, depending on the processingrequirements and/or the type of system, may be programmed to control anyof the processes disclosed herein, including the delivery of processinggases, temperature settings (e.g., heating and/or cooling), pressuresettings, vacuum settings, power settings, radio frequency (RF)generator settings, RF matching circuit settings, frequency settings,flow rate settings, fluid delivery settings, positional and operationsettings, wafer transfers into and out of a tool and other transfertools and/or load locks connected to or interfaced with a specificsystem.

Broadly speaking, the controller may be defined as electronics havingvarious integrated circuits, logic, memory, and/or software that receiveinstructions, issue instructions, control operation, enable cleaningoperations, enable endpoint measurements, and the like. The integratedcircuits may include chips in the form of firmware that store programinstructions, digital signal processors (DSPs), chips defined asapplication specific integrated circuits (ASICs), and/or one or moremicroprocessors, or microcontrollers that execute program instructions(e.g., software). Program instructions may be instructions communicatedto the controller in the form of various individual settings (or programfiles), defining operational parameters for carrying out a particularprocess on or for a semiconductor wafer or to a system. The operationalparameters may, in some embodiments, be part of a recipe defined byprocess engineers to accomplish one or more processing steps during thefabrication of one or more layers, materials, metals, oxides, silicon,silicon dioxide, surfaces, circuits, and/or dies of a wafer.

The controller, in some implementations, may be a part of or coupled toa computer that is integrated with, coupled to the system, otherwisenetworked to the system, or a combination thereof. For example, thecontroller may be in the “cloud” or all or a part of a fab host computersystem, which can allow for remote access of the wafer processing. Thecomputer may enable remote access to the system to monitor currentprogress of fabrication operations, examine a history of pastfabrication operations, examine trends or performance metrics from aplurality of fabrication operations, to change parameters of currentprocessing, to set processing steps to follow a current processing, orto start a new process. In some examples, a remote computer (e.g. aserver) can provide process recipes to a system over a network, whichmay include a local network or the Internet. The remote computer mayinclude a user interface that enables entry or programming of parametersand/or settings, which are then communicated to the system from theremote computer. In some examples, the controller receives instructionsin the form of data, which specify parameters for each of the processingsteps to be performed during one or more operations. It should beunderstood that the parameters may be specific to the type of process tobe performed and the type of tool that the controller is configured tointerface with or control. Thus as described above, the controller maybe distributed, such as by comprising one or more discrete controllersthat are networked together and working towards a common purpose, suchas the processes and controls described herein. An example of adistributed controller for such purposes would be one or more integratedcircuits on a chamber in communication with one or more integratedcircuits located remotely (such as at the platform level or as part of aremote computer) that combine to control a process on the chamber.

Without limitation, example systems may include a plasma etch chamber ormodule (employing inductively or capacitively coupled plasmas), adeposition chamber or module, a spin-rinse chamber or module, a metalplating chamber or module, a clean chamber or module, a bevel edge etchchamber or module, a physical vapor deposition (PVD) chamber or module,a chemical vapor deposition (CVD) chamber or module, an atomic layerdeposition (ALD) chamber or module, an atomic layer etch (ALE) chamberor module, an ion implantation chamber or module, a track chamber ormodule, and any other semiconductor processing systems that may beassociated or used in the fabrication and/or manufacturing ofsemiconductor wafers.

As noted above, depending on the process step or steps to be performedby the tool, the controller might communicate with one or more of othertool circuits or modules, other tool components, cluster tools, othertool interfaces, adjacent tools, neighboring tools, tools locatedthroughout a factory, a main computer, another controller, or tools usedin material transport that bring containers of wafers to and from toollocations and/or load ports in a semiconductor manufacturing factory.

OTHER EMBODIMENTS

Although the foregoing disclosed techniques, operations, processes,methods, systems, apparatuses, tools, films, chemistries, andcompositions have been described in detail within the context ofspecific embodiments for the purpose of promoting clarity andunderstanding, it will be apparent to one of ordinary skill in the artthat there are many alternative ways of implementing the foregoingembodiments which are within the spirit and scope of this disclosure.Accordingly, the embodiments described herein are to be viewed asillustrative of the disclosed inventive concepts rather thanrestrictively, and are not to be used as an impermissible basis forunduly limiting the scope of any claims eventually directed to thesubject matter of this disclosure.

What is claimed is:
 1. A method of generating a look-up table (LUT)associating, for a plurality of features on a semiconductor substratesurface, values of one or more quantities characteristic of an edgeplacement error (EPE) with values of one or more quantitiescharacteristic of an etch process, the features to be etched into amaterial stack on said substrate via a plasma-based etch processperformed in a processing chamber under a set of process conditions, themethod comprising: (a) receiving the set of process conditions and thematerial stack composition; (b) receiving a pattern of photoresistdefining a set of features; (c1) calculating, using a computer system, afirst etch process characteristic value, the first etch processcharacteristic value corresponding to a first quantity characteristic ofthe etch process, under the set of process conditions, of a firstselected feature from the set of features, wherein calculating the firstetch process characteristic is performed using a computer model thatrelates an etched feature profile on a semiconductor device to one ormore process conditions in an etcher; (c2) calculating, using a computersystem, a second etch process characteristic value, the second etchprocess characteristic value corresponding to the first characteristicof the etch process, under the set of process conditions, of a secondselected feature from the set of features, wherein calculating thesecond etch process characteristic is performed using the computermodel; and (d1) including a first entry in the LUT associated with anedge of the first selected feature, the first entry comprising: thefirst etch process characteristic value; and a first EPE-characteristic(EPC) value corresponding to a quantity characteristic of an EPE of theedge of the first selected feature, said first EPC value generated byrunning a computerized etch profile model (EPM) to simulate etchingunder the set of process conditions of the material stack as overlaidwith at least the portion of the pattern of photoresist corresponding tothe first selected feature; and (d2) determining to not include an entryin the LUT associated with an edge of the second selected feature andcomprising the second etch process characteristic value, the determiningbased, at least in part, on the similarity of the second etch processcharacteristic value to the first etch process characteristic value,wherein a LUT produced using (d1) and (d2) provides a computationallymore efficient tool for determining values of the one or more quantitiescharacteristic of edge placement error (EPE) in comparison to thecomputer model that relates an etched feature profile on a semiconductordevice to one or more process conditions.
 2. The method of claim 1,wherein it is determined in (d2) to not include the entry in the LUT forthe second selected feature when the second etch process characteristicvalue is within 5% of the first etch process characteristic value. 3.The method of claim 1, wherein it is determined in (d2) to not includethe entry in the LUT for the second selected feature when the secondetch process characteristic value is within 2% of the first etch processcharacteristic value.
 4. The method of claim 1, further comprising: (c3)calculating a third etch process characteristic value, the third etchprocess characteristic value corresponding to the first quantitycharacteristic of the etch process during the etch, under the set ofprocess conditions, of a third selected feature from the set offeatures; and (d3) determining to not include an entry in the LUTassociated with an edge of the third selected feature and comprising thethird etch process characteristic value, the determining based, at leastin part, on the similarity of the third etch process characteristicvalue to the first etch process characteristic value.
 5. The method ofclaim 4, wherein: in (d2) it is determined to not include the entry inthe LUT for the second selected feature when the second etch processcharacteristic value is within 5% of the first etch processcharacteristic value; and in (d3) it is determined to not include theentry in the LUT for the third selected feature when the third etchprocess characteristic value is within 5% of the first etch processcharacteristic value.
 6. The method of claim 1, further comprising:(c1′) calculating a third etch process characteristic value, the thirdetch process characteristic value corresponding to a second quantitycharacteristic of the etch process, under the set of process conditions,of the first selected feature; and (c2′) calculating a fourth etchprocess characteristic value, the fourth etch process characteristicvalue corresponding to the second quantity characteristic of the etchprocess, under the set of process conditions, of the second selectedfeature;  wherein: in (d1), the first entry in the LUT further comprisesthe third etch process characteristic value; and in (d2), thedetermining is further based on the similarity of the fourth etchprocess characteristic value to the third etch process characteristicvalue.
 7. The method of claim 6, wherein in (d2) it is determined to notinclude the entry in the LUT for the second selected feature when: thesecond etch process characteristic value is within 5% of the first etchprocess characteristic value; and the fourth etch process characteristicvalue is within 5% of the third etch process characteristic value. 8.The method of claim 6, wherein in (d2) the determining is based, atleast in part, on a distance metric calculated between the firstselected feature and the second selected feature, the distance metriccalculated by a procedure comprising: calculating a first differenceindicator (DI) value indicative of the difference between the first etchprocess characteristic value and the second etch process characteristicvalue; calculating a second DI value indicative of the differencebetween the third etch process characteristic value and the fourth etchprocess characteristic value; and calculating a combined DI valueindicative of the sum of the magnitudes of the first DI value and thesecond DI value.
 9. The method of claim 8, wherein in (d2) thedetermining comprises comparing the distance metric to a referencevalue.
 10. The method of claim 1, wherein in (d2) the determining isfurther based on the similarity of the first EPC value to a second EPCvalue, the second EPC value corresponding to a quantity characteristicof an EPE of the edge of the second selected feature, said second EPCvalue generated by running a computerized etch profile model (EPM) tosimulate etching under the set of process conditions of the materialstack as overlaid with at least the portion of the pattern ofphotoresist corresponding to the second selected feature.
 11. The methodof claim 1, wherein the first quantity characteristic of the etchprocess is a characteristic of in-feature plasma ion flux (IFPIF). 12.The method of claim 11, wherein the first etch process characteristicvalue is estimated based on a visibility kernel (VC) corresponding tothe feature.
 13. The method of claim 12, wherein the first etch processcharacteristic is calculated by a procedure comprising estimating theintegral of the VC with the ion energy angular distribution function(IEADF) corresponding to one or more plasma ion fluxes (PIF) above thefeature.
 14. The method of claim 1, wherein the first quantitycharacteristic of the etch process is a characteristic of in-featureplasma neutral flux (IFPNF).
 15. The method of claim 14, wherein thequantity characteristic of IFPNF is a loaded plasma flux above thefeature which accounts for the presence of the substrate in theprocessing chamber.
 16. The method of claim 1, wherein in (d2) thedetermining is further based on: a sensitivity metric characteristic ofthe magnitude of variations in the first EPC value which result fromchanges in the first etch process characteristic value; and/or asensitivity metric characteristic of the magnitude of variations in asecond EPC value which result from changes in the second etch processcharacteristic value, the second EPC value corresponding to a quantitycharacteristic of an EPE of the edge of the second selected feature,said value generated by running a computerized etch profile model (EPM)to simulate etching under the set of process conditions of the materialstack as overlaid with at least the portion of the pattern ofphotoresist corresponding to the second selected feature.
 17. The methodof claim 16, wherein the sensitivity metric characteristic of either orboth of the first or second EPC values is calculated by estimating thepartial derivative of the quantity characteristic of EPE with respect tothe first quantity characteristic of the etch process (d[EPE]/d[etchprocess]) evaluated at either the first or second values of the EPC andthe etch process characteristic.
 18. The method of claim 17, wherein thesensitivity metric is calculated by a process comprising: calculating afirst difference indicator (DI) value indicative of the differencebetween the first and second EPC values; calculating a second DI valueindicative of the difference between the first and second etch processcharacteristic values; and calculating a value indicative ofd[EPE]/d[etch process] by calculating a value indicative of the ratio ofthe second to the first DI values.
 19. The method of claim 18, whereinin (d2) the determining comprises comparing the sensitivity metric to areference value.
 20. The method of claim 19, wherein the first quantitycharacteristic of the etch process is a characteristic of in-featureplasma ion flux (IFPIF).
 21. The method of claim 19, wherein the firstquantity characteristic of the etch process is a characteristic ofin-feature plasma neutral flux (IFPNF).
 22. The method of claim 1,wherein the received set of process conditions include global processingchamber plasma fluxes of ion and/or neutral/radical plasma species. 23.The method of claim 1, further comprising: (e) using a LUT producedusing (d1) and (d2) to enable development of a lithographic mask usingvalues of EPC in the LUT, and/or to enable etching a semiconductorsubstrate using a set of etch conditions identified using values of EPCin the LUT.
 24. The method of claim 1, wherein operation (d)(2) limitsthe size of the LUT, thereby making the LUT more efficient to use.
 25. Alook-up table (LUT) comprising a plurality of entries corresponding to aplurality of edges of a plurality of features to be etched into amaterial stack on a semiconductor substrate surface via a plasma-basedetch process performed in a processing chamber under a set of processconditions, the entries comprising a plurality of fields, the fieldscomprising: an EPE field holding a value of a quantity characteristic ofan edge placement error (EPE); and one or more etch process fieldsholding values of one or more quantities characteristic of an etchprocess, the fields selected from: an IFPIF field for holding a value ofa quantity characteristic of in-feature plasma ion flux (IFPIF); anIFPNF field for holding a value of a quantity characteristic ofin-feature plasma neutral flux (IFPNF); and an IFPDF field for holding avalue of a quantity characteristic of in-feature passivant depositionflux (IFPDF); wherein the average relative difference between pairs ofnearest values held in fields of the table corresponding to eachquantity characteristic of the etch process is greater than 5%, whereinthe LUT provides a computationally more efficient tool for determiningvalues of the quantity characteristic of the EPE in comparison to acomputer model that relates an etched feature profile on a semiconductordevice to one or more process conditions, which computer model was usedto calculate values of EPE used in the LUT.